Marianna Apidianaki
email: marianna.apidianaki@inria.fr

Tim Van De

Cruys Alpage

A Quantitative Evaluation of Global Word Sense Induction

Word sense induction (WSI) is the task aimed at automatically identifying the senses of words in texts, without the need for handcrafted resources or annotated data. Up till now, most WSI algorithms extract the different senses of a word 'locally' on a per-word basis, i.e. the different senses for each word are determined separately. In this paper, we compare the performance of such algorithms to an algorithm that uses a 'global' approach, i.e. the different senses of a particular word are determined by comparing them to, and demarcating them from, the senses of other words in a full-blown word space model. We adopt the evaluation framework proposed in the SemEval-2010 Word Sense Induction & Disambiguation task. All systems that participated in this task use a local scheme for determining the different senses of a word. We compare their results to the ones obtained by the global approach, and discuss the advantages and weaknesses of both approaches.

Introduction

Word sense induction (WSI) methods automatically identify the senses of words in texts, without the need for predefined resources or annotated data. These methods offer an alternative to the use of expensive hand-crafted resources developed according to the 'fixed list of senses' paradigm, which present several drawbacks for efficient semantic processing [START_REF] Ide | Making sense about sense[END_REF]. The assumption underlying unsupervised WSI methods is the distributional hypothesis of meaning [START_REF] Harris | Distributional structure[END_REF], according to which words that occur in similar contexts tend to be similar. In distributional semantic analysis, the co-occurrences of words in texts constitute the features that serve to calculate their similarity. Following this approach, data-driven WSI algorithms calculate the similarity of the contexts of polysemous target words and group them into clusters. The resulting clusters describe the target word senses.

The unsupervised algorithms used for WSI can be distinguished into local and global. Local algorithms work on a per-word basis, determining the senses for each word separately. Algorithms that use a global approach determine the different senses of a particular word by comparing them to, and demarcating them from, the senses of other words in a full-blown word space model.

In this paper, we compare the performance of these two types of algorithms for sense induction. The comparison is carried out using the evaluation framework proposed in the SemEval-2010 Word Sense Induction & Disambiguation (WSI&D) task [START_REF] Manandhar | Semeval-2010 task 14: Evaluation setting for word sense induction & disambiguation systems[END_REF][START_REF] Manandhar | Semeval-2010 task 14: Word sense induction &disambiguation[END_REF]. The SemEval WSI tasks [START_REF] Manandhar | Semeval-2010 task 14: Word sense induction &disambiguation[END_REF][START_REF] Agirre | Semeval-2007 task 02: Evaluating word sense induction and discrimination systems[END_REF] provide a common ground for comparison and evaluation of different sense induction and discrimination systems. All the systems that participated in the SemEval-2010 WSI&D task use a local scheme for determining the different senses of a word. We compare their results to the ones obtained by the global approach, and discuss the advantages and weaknesses of both approaches.

The paper is organized as follows. We first explain how word senses are identified in the local and the global approaches to sense induction, and we present the global algorithm used in our research. Section 3 describes the evaluation setting that we adopt and the metrics that will be used in order to evaluate the performance of the algorithms. In Section 4, we present the evaluation results of the global approach, and compare them to the results obtained by the local systems that participated in the SemEval-2010 WSI&D task. Our last section draws conclusions, and lays out some avenues for future work.

WSI algorithms

Inducing word senses on a per-word basis

Local methods to word sense induction discover the senses of a target word (w ) by clustering its instances in texts according to their semantic similarity. Following the distributional hypothesis of meaning, words that are used in similar contexts carry similar meanings [START_REF] Harris | Distributional structure[END_REF][START_REF] Miller | Contextual correlates of semantic similarity[END_REF]. So, the instances of w that appear in similar contexts are considered as semantically similar and its senses can be discovered by clustering its contexts [START_REF] Navigli | Word sense disambiguation: a survey[END_REF].

The features used for calculating the similarity of the instances of w are their co-occurrences in a fixed-sized window of text. So, the different instances of w in a corpus can be represented by feature vectors created from their contexts [START_REF] Schütze | Automatic word sense discrimination[END_REF][START_REF] Purandare | Word sense discrimination by clustering contexts in vector and similarity spaces[END_REF]. The grouping of the context vectors according to their similarity generates a number of clusters that describe the different senses of w. The context of w may be taken into account in different ways : it may be modeled as a firstorder context vector, representing the direct context of the instances of w in the corpus [START_REF] Pedersen | Distinguishing word senses in untagged text[END_REF][START_REF] Bordag | Word sense induction: Triplet-based clustering and automatic evaluation[END_REF], or by using higher-order vectors, i.e. by considering the context vectors of the words occurring in the target context [START_REF] Schütze | Automatic word sense discrimination[END_REF].

Other methods use the words found in the context of target words in order to construct co-occurrence graphs. In a graph of this type, the vertices correspond to the words appearing in the contexts of the target words and the edges represent their relations. These relations may be grammatical [START_REF] Widdows | A graph model for unsupervised lexical acquisition[END_REF] or they may be cooccurrences of the words in fixed contexts [START_REF] Véronis | Hyperlex: lexical cartography for information retrieval[END_REF][START_REF] Agirre | Two graph-based algorithms for state-of-the-art wsd[END_REF]. The senses of the target words are discovered by partitioning the co-occurrence graph using clustering techniques, or by using a PageRank algorithm.

Global approach to sense induction

In contrast to the local approach to sense induction, where senses are discovered by clustering contexts for each word individually, the global approach discovers senses by clustering semantically similar senses of words in a global manner, comparing them and demarcating them from the senses of other words in a fullblown word space model. The similarity between the senses is calculated on the basis of their common features, e.g. the syntactic dependencies a particular sense occurs with [START_REF] Lin | Automatic retrieval and clustering of similar words[END_REF].

In Pantel and Lin's [START_REF] Pantel | Discovering word senses from text[END_REF] method, the similarity of word senses is calculated on the basis of the dependency relations in which the senses take part (extracted from a syntactically annotated corpus). Each word is represented by a feature vector, where each feature corresponds to a syntactic context (dependency triple) in which the word occurs. Each feature is weighted and its value corresponds to the pointwise mutual information between the feature and the word. The algorithm first discovers a set of tight clusters (called 'committees') in the similarity space. Each word is then assigned to the closest committee by comparing the word's feature vector to the centroid of a committee (i.e. the mean of the feature vectors of the committee members). After a word is assigned to a particular committee, the overlapping features are deleted from the word's vector, which allows for the discovery of less dominant senses. Each cluster that a word belongs to describes one of its senses.

Non-negative Matrix Factorization for sense induction

Sense induction The global algorithm implemented here is based on the one proposed by Van de Cruys [START_REF] Van De Cruys | Using three way data for word sense discrimination[END_REF]. This algorithm creates semantic word models by using an extension of non-negative matrix factorization (NMF) [START_REF] Lee | Algorithms for non-negative matrix factorization[END_REF], that combines both the bag of words approach and the syntax-based approach to sense induction. The intuition in this is that the syntactic features of the syntax-based approach can be disambiguated by the semantic dimensions found by the bag of words approach. The algorithm finds a small number of latent semantic dimensions, according to which nouns, contexts and syntactic relations are classified.

Nouns are classified according to both bag-of-words context and syntactic context, so three matrices are constructed that capture the co-occurrence frequency information for each mode. The first matrix contains co-occurrence frequencies of nouns cross-classified by dependency relations, the second matrix contains co-occurrence frequencies of nouns cross-classified by words that appear in the noun's context window, and the third matrix contains co-occurrence frequencies of dependency relations cross-classified by co-occurring context words. NMF is then applied to the three matrices and the separate factorizations are interleaved (i.e. the results of the former factorization are used to initialize the factorization of the next matrix). A graphical representation of the interleaved factorization algorithm is given in figure 1.

When the factorization is finished, the three different modes (nouns, bagof-words context words and syntactic relations) are all represented as a limited number of semantic dimensions. Next, the factorization that is thus created is used for word sense induction. The intuition is that a particular dimension of an ambiguous word is 'switched off', to reveal possible other senses of the word. Matrix H indicates the importance of each syntactic relation given a semantic dimension. With this knowledge, the syntactic relations that are responsible for a certain dimension can be subtracted from the original noun vector. This is done by scaling down each feature of the original vector according to the load of the feature on the subtracted dimension.

The last step is to determine which dimension(s) are responsible for a certain sense of the word. In order to do so, the method is embedded in a clustering approach. First, a specific word is assigned to its predominant sense (i.e. the most similar cluster). Next, the dominant semantic dimension(s) for this cluster are subtracted from the word vector, and the resulting vector is fed to the clustering algorithm again, to see if other word senses emerge. The dominant semantic dimension(s) can be identified by 'folding in' the cluster centroid into the factorization.

A simple k-means algorithm is used to compute the initial clustering. kmeans yields a hard clustering, in which each noun is assigned to exactly one (dominant) cluster. In the second step, it is determined for each noun whether it can be assigned to other, less dominant clusters. First, the salient dimension(s) of the centroid to which the noun is assigned are determined. The centroid of the cluster is computed by averaging the frequencies of all cluster elements except for the target word we want to reassign, and weighting the resulting vector with pointwise mutual information [START_REF] Church | Word association norms, mutual information & lexicography[END_REF]. After subtracting the salient dimensions from the noun vector, it is checked whether the vector is reassigned to another cluster centroid. If this is the case, (another instance of) the noun is assigned to the cluster, and the second step is repeated. If there is no reassignment, we continue with the next word. The target element is removed from the centroid to make sure that only the dimensions associated with the sense of the cluster are subtracted. When the algorithm is finished, each noun is assigned to a number of clusters, representing its different senses.

We use two different methods for selecting the final number of candidate senses. The first method, NMF con , takes a conservative approach, and only selects candidate senses if -after the subtraction of salient dimensions -another sense is found that is more similar to the adapted noun vector. The second method, NMF lib , is more liberal, and also selects the next best cluster centroid as candidate sense until a certain similarity threshold φ is reached. Experimentally (examining the cluster output), we set φ = 0.2 .

Sense disambiguation

The sense inventory that results from the induction step can now be used for the disambiguation of individual instances as follows.

For each instance of the target noun, we extract its context words, i.e. the words that co-occur in the same paragraph, and represent them as a frequency vector. Using matrix G from our factorization model (which represents context words by semantic dimensions), this co-occurrence vector can be 'fold in' into the semantic space, thus representing the probability of each semantic dimension for the particular instance of the target noun. Likewise, the candidate senses of the noun (represented as centroids) can be folded into our semantic space using matrix H, which represents the dependency relations by semantic dimensions. This yields a probability distribution over the semantic dimensions for each centroid. As a last step, we compute the Kullback-Leibler divergence between the context vector and the candidate centroids, and select the candidate centroid that yields the lowest divergence as the correct sense.

Example Let us clarify the process with an example for the noun chip. The sense induction algorithm finds the following candidate senses:

1. cache, CPU, memory, microprocessor, processor, RAM, register 2. bread, cake, chocolate, cookie, recipe, sandwich 3. accessory, equipment, goods, item, machinery, material, product, supplies Each candidate sense is associated with a centroid (the average frequency vector of its members), that is fold into the semantic space, which yields a 'semantic fingerprint', i.e. a distribution over the semantic dimensions. For the first sense, the 'computer' dimension will be the most important. Likewise, for the second and the third sense the 'food' dimension and the 'manufacturing' dimension will be the most important. 1Let us now take a particular instance of the noun chip, such as the one in (1).

(1)

An N.V. Philips unit has created a computer system that processes video images 3,000 times faster than conventional systems. Using reduced instructionset computing, or RISC, chips made by Intergraph of Huntsville, Ala., the system splits the image it 'sees' into 20 digital representations, each processed by one chip.

Looking at the context of the particular instance of chip, a context vector is created which represents the semantic content words that appear in the same paragraph (the extracted content words are printed in boldface). This context vector is again folded into the semantic space, yielding a distribution over the semantic dimensions. By selecting the lowest Kullback-Leibler divergence between the semantic probability distribution of the target instance and the semantic probability distributions of the candidate senses, the algorithm is able to induce the 'computer' sense of the target noun chip.

Implementational details The SemEval training set has been part of speech tagged and lemmatized with Stanford Part-Of-Speech Tagger [START_REF] Toutanova | Enriching the knowledge sources used in a maximum entropy part-of-speech tagger[END_REF][START_REF] Toutanova | Feature-rich part-of-speech tagging with a cyclic dependency network[END_REF], and parsed with MaltParser [START_REF] Nivre | Maltparser: A data-driven parser-generator for dependency parsing[END_REF] trained on sections 2-21 of the Wall Street Journal section of the Penn Treebank extended with about 4000 questions from the QuestionBank2 in order to extract dependency triples. The SemEval test set has only been tagged and lemmatized, as our disambiguation model did not use dependency triples as features (contrary to our induction model).

The three matrices needed for our factorization model were constructed using the 5K nouns, 80K dependency relations, and 2K context words (excluding stop words) with highest frequency in the training set, which yields matrices of 5K nouns × 80K dependency relations, 5K nouns × 2K context words, and 80K dependency relations × 2K context words. For our initial k-means clustering, we cluster the 5K nouns into 600 clusters.

The sense induction and disambiguation algorithms were implemented in Python. The interleaved NMF factorization model itself was implemented in Matlab, using 50 iterations, and factorizing the model to 50 dimensions.

3 Word sense induction evaluation in SemEval 2010

Training and evaluation datasets

Our WSI algorithm is trained and tested on the dataset of the SemEval-2010 WSI&D task [START_REF] Manandhar | Semeval-2010 task 14: Word sense induction &disambiguation[END_REF]. The main difference of this task from the SemEval-2007 WSI task [START_REF] Agirre | Semeval-2007 task 02: Evaluating word sense induction and discrimination systems[END_REF] is that the training and testing data are treated separately, which allows for a more realistic evaluation of the clustering models. Word senses are induced from the training data while testing data are used for tagging new instances of the words with the previously discovered senses.

The SemEval-2010 WSI&D task is based on a dataset of 100 target words, 50 nouns and 50 verbs. For each target word, a training set is provided from which the senses of the word have to be induced without using any other resources. The training set for a target word consists of a set of target word instances in context (sentences or paragraphs). In this paper, we will focus on the set of nouns, that consists of 716,945 instances.

The senses induced during training are used for disambiguation in the testing phase. In this phase, the systems are provided with a testing dataset that consists of unseen instances of the target words. The testset comprises 5,285 noun instances. The instances in the testset are tagged with OntoNotes senses [START_REF] Hovy | Ontonotes: the 90% solution[END_REF]. The systems need to disambiguate these instances using the senses acquired during training.

Supervised and unsupervised evaluation

The results of the systems participating in the SemEval-2010 WSI&D task are evaluated both in a supervised and in an unsupervised manner. In the supervised evaluation, one part of the testing dataset is used as a mapping corpus, which serves to map the automatically induced clusters to gold standard (GS) senses, and the other part as an evaluation corpus, used to evaluate the methods in a standard WSD task. The mapping between clusters and GS senses serves to tag the evaluation corpus with GS tags.

In the unsupervised evaluation, the induced senses are evaluated as clusters of examples (tw contexts) which are compared to the sets of examples tagged with the GS senses (corresponding to classes). So, if the testing dataset of a tw comprises a number of instances, these are divided into two partitions : a set of automatically generated clusters and a set of GS classes. A number of these instances will be members of both one GS class and one cluster. Consequently, the quality of the proposed clustering solution is evaluated by comparing the two groupings and measuring their similarity.

Evaluation measures

The supervised evaluation in the SemEval-2010 WSI&D task follows the scheme employed in the SemEval-2007 WSI task [START_REF] Agirre | Semeval-2007 task 02: Evaluating word sense induction and discrimination systems[END_REF], with some modifications. The induced senses (clusters) are mapped to GS senses using a mapping corpus, which is a part of the testing sense-tagged dataset. Then, the evaluation corpus, which corresponds to the rest of the testing dataset, is used to evaluate WSI methods in a standard WSD task. The evaluation is performed according to the precision and recall measures employed for the evaluation of supervised WSD systems.

Two evaluation metrics are employed during the unsupervised evaluation in order to estimate the quality of the clustering solutions, the V-measure [START_REF] Rosenberg | V-measure: A conditional entropy-based external cluster evaluation measure[END_REF] and the paired F-Score [START_REF] Artiles | The role of named entities in web people search[END_REF]. V-Measure assesses the quality of a clustering by measuring its homogeneity (h) and its completeness (c). Homogeneity refers to the degree that each cluster consists of data points primarily belonging to a single GS class, while completeness refers to the degree that each GS class consists of data points primarily assigned to a single cluster. V-Measure is the harmonic mean of h and c.

V M = 2 • h • c h + c (1)
In the paired F-Score [START_REF] Artiles | The role of named entities in web people search[END_REF] evaluation, the clustering problem is transformed into a classification problem [START_REF] Manandhar | Semeval-2010 task 14: Word sense induction &disambiguation[END_REF]. A set of instance pairs is generated from the automatically induced clusters (F(K)), which comprises pairs of the instances found in each cluster. Similarly, a set of instance pairs is created from the GS classes (F(S)), containing pairs of the instances found in each class. Precision is then defined as the number of common instance pairs between the two sets to the total number of pairs in the clustering solution (cf. formula 2). Recall is defined as the number of common instance pairs between the two sets to the total number of pairs in the GS (cf. formula 3). Precision and recall are finally combined to produce the harmonic mean (cf. formula 4).

P = |F (K) ∩ F (S)| |F (K)| (2) R = |F (K) ∩ F (S)| |F (S)| (3)
F S = 2 • P • R P + R (4)
The obtained results are also compared to two baselines. The Most Frequent Sense (MFS ) baseline groups all testing instances of a tw into one cluster. The Random baseline randomly assigns an instance to one of the clusters. 3 . This baseline is executed five times and the results are averaged.

Evaluation results

Unsupervised evaluation

In table 1, we present the performance of a number of algorithms on the Vmeasure. We compare our V-measure scores with the scores of the best-ranked systems in the SemEval 2010 WSI&D task. The second column shows the number of clusters induced in the test set by each algorithm. The MFS baseline has a V-Measure equal to 0, since by definition its completeness is 1 and homogeneity is 0.

NMF con -our model that takes a conservative approach in the induction of candidate senses -does not beat the random baseline. NMF lib -our model that is more liberal in inducing senses -reaches better results. With 13.5%, it scores similar to other algorithms that induce a similar average number of clusters, such as Duluth-WSI [START_REF] Pedersen | Duluth-wsi: Senseclusters applied to the sense induction task of semeval-2[END_REF].

Pedersen [START_REF] Pedersen | Duluth-wsi: Senseclusters applied to the sense induction task of semeval-2[END_REF] has shown that the V-Measure tends to favour systems producing a higher number of clusters than the number of GS senses. This is reflected in the scores of our models as well. In table 2, the paired F-Score of a number of algorithms is given. The paired F-Score penalizes systems when they produce a higher number of clusters (low recall) or a lower number of clusters (low precision) than the GS number of senses. We again compare our results with the scores of the best-ranked systems in the SemEval 2010 WSI&D task. NMF con reaches a score of 54.6%, which is again similar to other algorithms that induce the same average number clusters. NMF lib scores 42.2%, indicating that the algorithm is able to retain a reasonable F-Score while at the same time inducing a significant number of clusters. This especially becomes clear when comparing its score to the other algorithms.

Supervised evaluation

Table 3 shows the recall of our algorithms in the supervised evaluation, again compared to other algorithms evaluated in the SemEval 2010 WSI&D task.

NMF lib gets 57.3% and NMF con reaches 54.5%, which again indicates that our algorithm is in the same ballpark as other algorithms that induce a similar average number of senses.

Conclusion and future work

In this paper, we presented a quantitative evaluation of a global approach to word sense induction, and compared it to more prevailing local approaches to word sense induction, that induce senses on a per-word basis. The results indicate that the global approach performs equally well, reaching similar results to the stateof-the-art performance of local approaches. Moreover, the global approach is able to reach similar performance on an evaluation set that is tuned to fit the needs of local approaches. The evaluation set contains an enormous amount of contexts for only a small number of target words, favouring methods that induce senses on a per-word basis. The global approach is likely to induce a more balanced sense inventory using a more balanced, unbiased corpus, and is likely to outperform local methods when such an unbiased corpus is used as input. We therefore think that a global approach to word sense induction, such as the one presented here, provides a genuine and powerful solution to the problem at hand, and deserves further attention. We conclude with some issues for future work. First of all, we would like to evaluate the approach presented here using a more balanced an unbiased corpus, and compare its performance on such a corpus to local approaches. Secondly, we would also like to include grammatical dependency information in the disambiguation step of the algorithm. For now, the disambiguation step only uses a word's context words; enriching the feature set with dependency information is likely to improve the performance of the disambiguation.

Fig. 1 .

 1 Fig. 1. A graphical representation of the extended nmf

Table 1 .

 1 V-measure for SemEval noun testset

		VM (%) #Cl
	UoY	20.6	11.54
	Hermit	16.7	10.78
	KSU KDD	18.0	17.5
	NMF lib	13.5	5.42
	Duluth-WSI	11.4	4.15
	Random	4.2	4.00
	NMFcon	3.9	1.58
	MFS	0.0	1.00

Table 2 .

 2 Paired F-score for SemEval noun testset

		FS (%) #Cl
	MFS	57.0 1.00
	Duluth-WSI-SVD-Gap 57.0 1.02
	NMFcon	54.6 1.58
	NMF lib	42.2 5.42
	Duluth-WSI	37.1 4.15
	Random	30.4 4.00

Table 3 .

 3 Supervised recall for SemEval noun testset, 80% mapping, 20% evaluation

		SR (%) #S
	UoY	59.4 1.51
	NMF lib	57.3 1.93
	Duluth-WSI 54.7 1.66
	NMFcon	54.5 1.21
	MFS	53.2 1.00
	Random	51.5 1.53

In the majority of cases, the induced dimensions indeed contain such clear-cut semantics, so that the dimensions can be rightfully labeled as above.

http://maltparser.org/mco/english_parser/engmalt.html

The number of clusters of Random was chosen to be roughly equal to the average number of senses in the GS.

Acknowledgments

This work is supported by the Scribo project, funded by the French "pôle de compétitivité" System@tic, and by the French national grant EDyLex (ANR-09-CORD-008).


Michel Busquet
email: busquet@artepinc.com

Frédéric Thais

Matthias González

Edouard Audit

Measure of precursor electron density profiles of laser launched radiative shocks

Keywords:

We have studied the dynamics of strong radiative shocks generated with the highenergy sub-nanosecond iodine laser at PALS facility (Prague) over long time scales, up to 100 ns. These shock waves are characterized by a developed radiative precursor: a radiation driven ionization wave in front of the density jump of the shock. Electronic density profiles are measured at different times after the laser pulse and at different distances from the axis of the shock tube. A new feature, described as a split precursor, has been observed. Comparisons with 2D computations are shown.

-INTRODUCTION

Radiative shocks [START_REF] Zeldovich | Physics of Shock Waves and High Temperature Hydrodynamic Phenomena[END_REF] are strong shocks where the flux of ionizing photons coming from the shock front is large enough to launch an ionization wave in front of the shock. This radiative precursor heats the medium in front of the density jump to a temperature often equal to the temperature of the shocked medium. Radiative-precursor shocks are relevant to astrophysics, in supernova [2], supernova remnants [3], accretion shocks [START_REF] Bouvier | Magnetospheric Accretion In Classical T Tauri Stars[END_REF] and jets [5]. A criterion for a velocity threshold of radiative precursors has been derived balancing downstream ionizing photons and upstream atoms being ionized [6]. Radiative shocks have been produced in the laboratory at laser facilities with blast waves in residual gas inside the vacuum chamber [7], or with shock waves in foam [8], or in gas filled mini-shock tubes [9,10,11], where the shock is launched by a laser ablated foil acting as a piston. Scaled down to the laboratory, as the attainable velocity is ruled by the available laser energy, the velocity threshold criterion lead to use high atomic number gas, Argon or Xenon, at low pressure (0.05 -5 bar). Studies of radiative shocks in Xenon have been initiated on the CEA-Limeil facility [12], followed by experiments on the LULI facility [9] and on the Omega facility [10].

Recently we achieved the first long time observation (over 40 ns) on the PALS facility [11].

In the study we are presenting here, time of analysis is even larger, as we observe the radiative precursor up to 100 ns and we measure electron density profiles up to 50 ns, with various plasma conditions and observation geometries. Preliminary results have been presented elsewhere [START_REF] Stehle | Experimental study of radiative shocks at PALS facility[END_REF], in this paper we go into more detailed analysis, including synthetic interferogram, and complete or correct some values, leading to a refined conclusion.

-EXPERIMENTAL SETUP AND SOME THEORY ABOUT RADIATIVE SHOCKS

The experiment was performed at the Prague Asterix Laser System facility (PALS) [14]. The experimental setup (Fig. 1) includes two main diagnostics : a time resolved interferometer using a green laser (!=0.527 !m) to probe the electron density in the radiative precursor and a time-integrated backside XUV spectroscopy. The frequency tripled (! 3 =0.438 !m) laser pulse of the PALS iodine laser is focused on the target, a miniaturized shock tube described below. The nominal pulse conditions are a 0.35 ns duration and a 150-170 J energy (in green) after the infrared rejecting filter. The 29 cm diameter PALS beam is smoothed by a Phase Zone Plate (PZP) [15], located before the main PALS focalization lens.

The PZP yields a flat top focal spot of 0.55 mm FWHM in diameter, with 90% of the energy in a 0.7 mm circle, matching the inner section of the smallest shock tubes. Accounting for an incomplete transmission for each of the PZP, the focusing lens and the vacuum window, the resulting energy on target is 110-130 J. Then mean laser intensity on target is 10 14 W/cm 2 in green (! 3 =0.438 !m).

Figure 1 : experimental setup (see text for details).

We use miniaturized shock tubes (Fig. 2) filled with Xenon at low pressure (or air-Xenon mixtures in some case). The specially designed targets [16] were manufactured at "Pôle Instrumental de l'Observatoire de Paris". Two geometries have has been used :

- The PALS laser, focalized on the foil hereafter called piston, ablates the polystyrene.

Following the ablation, the piston is accelerated by rocket effect and launch a strong, radiating shock in the Xenon gas [9]. The gold coating of the piston contributes to half of the inertia of the piston, but its first use is to block preheating of the Xenon gas by hard x-rays originated from the laser interaction region. However, experimental results suggest that the back layers of the gold coating may undergo a small preheating.

In front of the pure hydrodynamic density jump, a radiation driven ionization wave is launched: the radiative precursor. Electron density increase in the radiative precursor is due to increased ionization, following the increased temperature, but the ion density is unchanged.

Typical profiles computed with the one-dimensional hydrodynamic code MULTI [18,[START_REF] Busquet | An Extended Version of the MULTI Code[END_REF] are displayed in Fig. 3 . [18,[START_REF] Busquet | An Extended Version of the MULTI Code[END_REF] For the time resolved interferometric diagnostics, we use an auxiliary laser working at ! P =527 nm, with a pulse duration of ~ 300 ns. The probe beam is expanded to cover more that the tube length. The target is located in one arm of a Mach-Zehnder interferometer. The recombined two beams of the interferometer are imaged on the slit of a micro-channel plate enhanced streak camera with a CCD imaging camera (512 x 512 pixels). Interferometric filter at !=527 nm and color glass filter located in front of the slit prevent any parasitic contribution from the plasma self-emission or from stray light from the main laser. Two configurations are used (Fig. 2): (i) In the longitudinal configuration, we image the symmetry axis of the shock tube on the slit of the camera in order to record the shock propagation in the tube. (ii) In the transverse configuration, we image a section of the tube, perpendicular to the canal axis, to monitor the transverse shape of the shock wave by recording its time of arrival versus distance x from axis, at some fixed distance z o from the piston initial position. The observed regions in the two cases are displayed in Fig. 2 by crosshatched areas.

For this interferometric diagnostic, we use targets with various parameters : in the first type of targets studied in this paper, labeled CF7 and CF20 in Table I, the shock tube is limited by gold coated aluminium on two sides of the square section and by glass optical windows on the two other sides, coated with a 15 nm lining of gold. The glass windows allow interferometric diagnostics with the PALS auxiliary green laser as a probe beam. The internal section of this 6 mm long square channel is 0.7 x 0.7 mm 2 . The two other targets presented here, labeled CF61 and CF59 are similar to the previous ones, but with a wider internal section of 1.2 x 1.2 mm 2 , with 2 bulk aluminium sides and 2 aluminized glass windows. They have been used for "transverse" interferometry. The shock propagates in Xenon with aluminum limiting walls for these last two targets CF61 and CF59, whereas it propagates between gold walls in the first targets CF7 and CF20. The nature of the channel coating affects the albedo and thus has an impact on the radiation energy lost from the shock and therefore on the velocity of the precursor front [11,[START_REF] Leygnac | [END_REF]21]. Actually, regarding radiation transport, the wall material acts as pure gold or as alumina (Al 2 O 3 ). Specific experiments to access direct measure of the albedo have been performed since and are presented elsewhere. [22] We present measures of the electron density profiles in the next two sections.

-LONGITUDINAL INTERFEROMETRY

In the longitudinal configuration, time resolved interferometry traces the variation of the optical refraction index n(!), at the wavelength ! of the probe laser, versus the position z on the cell axis along the direction of the shock propagation, and integrated over the path of the probe laser (y direction) along the cell width. In plasmas, the variation of the optical index, n(!), is usually attributed to free electrons, and is function of the electron density N e ,

n(!) = [ 1-N e / N c, ! )] 1/2 ~ 1 -0.5 N e / N c, ! (1)
where N c, ! is the critical density at the wavelength ! of the probe laser. Thus, interferometry allows to measure the electron density < N e > as a function of the position z and time t , averaged over the transverse section d of the plasma

< N e (z, t) >= N e ( y, z, t) canal !width ! dy / d (2)
where "z" is the distance from the initial position of the piston along the direction of propagation and "y" is the transverse position in the direction of the laser probe beam.

In the longitudinal configuration, we set the slit in front of the camera to image only the very center of the tube. Slit width was generally ~100 microns.

3-1 qualitative analysis

We first present in this section results obtained with the interferometric diagnostic for the target CF7, shot #1029_07, filled with Xenon at 0.1 bar. The "post mortem" analysis of the target indicates a correct centering of the main laser impact. The x-ray pinhole image shows a smooth distribution of the laser intensity on the target. Raw image and processed interferogram are displayed in Fig. 4 . The probe intensity profile (derived from the record at late times) is substracted to the raw image without (Fig. 4b) or with additional FFT filtering removing high spatial frequency (as used in Fig. 9). The vertical axis is the time running for 100 ns from the bottom of the image. In this particular shot the laser pulse arrive just at the beginning of the sweep. The horizontal axis is the distance z from the initial position of the piston, located on the left of the figure. The 6 mm length of the canal is imaged on the whole slit and correspond to the full width of the image. The plasma plume ablated from the piston front side is not imaged in the observed spatial range. The horizontal bean-like dark areas are burnt pixels of the CCD. Low frequency filtering can remove them, but would smear out broadened fringes (around z=1.5mm and t=10ns) as well as pattern shifted by one half-period (around z=4.5mm and t=25ns).

Initial fringe shift, in zone "a" (lower part of Figs.4,5) at early times is attributed to electromagnetic perturbation to the camera electronic tube due to the plasma breakout.

Therefore reference position of the fringes will be taken after the perturbation. The interferogram presents two distinct zones of moving fringes. In zone "d" (t=40 to 60 ns, z=3 to 4 mm), the inclined fringes pattern is the signature of an electron density gradient, and is attributed to the radiative precursor [9]. The precursor foot (line "A"), where the fringes start to shift, is recorded at an average velocity around ~85 km/s, decreasing from an initial velocity of 120±20 km/s to a mere 60 km/s 4 ns later.

On the lower right (z>4.5mm) another front is seen, with sub-fronts detected (lines Gx), moving away from the rear of the miniature shock tube. This is attributed to another radiative shock (with a velocity of ~30km/s decreasing to ~10 km/s) launched by some faint preheat of the rear side window. The different patterns of the shifted fringes correspond to the sign of the density gradient as discussed in Koenig et al. [23]. Various interpretations can be proposed for the heating of the back window within a few ns from the laser pulse: fast electrons, suprathermal x-rays, residual laser light going through or around the piston. Preheating by fast electron occurs usually at higher laser intensities than the nominal value of our experiments (10 14 W/cm 2 ). Suprathermal x-rays are stopped by the gold layer and would not transport enough energy to ablate the back window. Suprathermal electrons or x-rays would probably equally preheat inner sides of lateral windows and back side window, whereas recorded interferograms evidence no perturbation before the direct and reverse radiative waves have traveled from their birth points. Furthermore, heating of lateral windows would squeeze the free channel, whereas heating of the back window launch an upstream wave. Because of the chromaticity of the focusing lens, the unconverted infrared (1") beam has a transverse size of 1 cm 2 at the target location, compared to the 0.5 mm 2 section of the tube. With less than 3J of unconverted light, it results that only a few mJ of infrared might go inside the tube and cannot launch an ionization wave. Heating from a fraction of Joule of residual converted (green) laser light going through tiny holes of the gold coating, or a few J in the wings of the PZP image going around the piston, is more likely. We have checked with an improved version [START_REF] Busquet | An Extended Version of the MULTI Code[END_REF] of the hydro code MULTI [18] that 0.1-0.2% of the incident energy can heat the end of the tube and launch a radiative wave. However, it was not possible to account for the exact complex geometry of the tube end, probably responsible of the sub-fronts launch. In the leftmost part of zone "d", we observed that the fringes, initially shifting to the right, start to shift back, following the decrease with time of the electron density: fringes inclined to the right (resp. to the left) means increasing density (resp. decreasing) with time.

This increasing-decreasing density feature is associated with preheating of the gold layer on the back side of the piston, inducing a small heat wave in the gas, as figured out from MULTI simulations. This observation comforts our confidence that the position of the piston is located at the end of the observable fringes (line C) after the obscure region "c" where the electron density in front of the piston (i.e. facing the laser) is large enough to absorb consequently the probe beam and to shift fringes more than observable. Synthetic interferogram (see discussion in the last paragraph of this section) confirms this analysis.

The more or less flat area "e" is understood as a split precursor, when an ionization wave is progressively detached from the main precursor (Fig. 6). This feature has not been seen with MULTI simulations using gray radiative transfer, as it is probably the results of spectral dependence of the radiative transfer. Multi-group, multi-dimensional numerical simulations will be carried out, using new methods in the HERACLES [25] code (implementation in progress) to address this question. Note that ahead of a diffusion radiation wave (a Marshak wave), there is generally a small foot, an exponentially decaying freestreaming region created by the high energy tail (relatively to the local temperature) of the photon distribution. This foot is the seed of the diffusive wave, well distinguished by the concavity of the temperature profile (downward for the diffusive wave, and upward for the seeding foot), whether the diffusive wave remains single or is progressively split in two because of steep variation with energy of the photon mean free path. An exponential decaying foot does not produce this plateau feature seen in the interferogram. At this time, we have no definite interpretation of this split precursor, but only a clear unambiguous observation of the phenomenon.

All these features have been identified on other shots, with different target conditions.

In shot #1030_05 (Fig. 7), the fill gas was a 50-50 mixture of Xenon and air , pressure was 0.17 bar. It displays a split precursor signature (V-shaped flat fringe between 2 zones of parallel fringes with different slopes), and a backwards precursor coming from the bottom of the tube. Slow down of the main precursor after shock crossing is equally clearly seen. effects with an approximation of the lateral radiative losses [24]. The computed final slope of the precursor is sensitive to the wall albedo used in the simulation. Here we used 60% with an equivalent diameter of 700 microns. When including a fraction of Joule deposited in the gold layer of the piston, we even observe (Fig. 8b) in the synthetic interferogram the commas seen in zone "d", revealing increase of electron density followed in time by some density decrease, in Xenon close to the piston. Exact structure of this energy deposition is not known, so precise shape of these comma features has not been reproduced. The split precursor region is not reproduced in this simulation. It probably requires multi-group radiation transfer to show up.

3-2 quantitative analysis

Using the processed image (Fig. 9) where we plot the position of the fringe maxima, we are able to follow the fringes displacement versus time. We can then derive the contour lines of the electron density as the phase shift follows the average electron density over the d=0.7 mm width of the tube :

!(z, t) = 2" d # ! ! ! 1 $ 1 $ N e (y, z, t) N c,# % & ' ' ( ) * * !dy! 0 d + , " d # !! ! N e (y, z, t)!dy!/! N c,# ! 0 d + =!" d # !<N e (z,t)>! ! N c,# ! , ( 3
)
where ! is the wavelength of the probe laser (here ! = 527 nm) and the average (for a given z) electron density <N e (z,t)> is given by Eq. ( 2).

The precursor front, taken at the position where the fringes are shifted by 1/10 period corresponding to <Ne>= 7 10 17 , shows a deceleration with time. Initial velocity is larger than 130 km/s, slowing down to ~90km/s after the full buildup of the precursor (between 2 and 3.5 mm from initial position of the piston) and then around 60 km/s. The reconstructed contour lines of the electronic density <N e (z,t)> (averaged over the width of the canal) are reported in Fig. 9 for values between 0.7 10 18 and 10 19 cm -3 . Fringes have almost the same slope between 20 and 50-60 ns, a signature of a stationary gradient length. At this time, the precursor front velocity is measured around ~90 km/s. Previous studies [11,[START_REF] Leygnac | [END_REF]21] have shown that the lateral radiative losses have an important role in the shock structure and dynamics. In particular, the precursor velocity is much slower when there are lateral losses, and slows down until it has reached a stationary limit with then a velocity equal to the velocity of the hydrodynamic shock (i.e. density jump). This limit has not been reached in our experiment before the main precursor crosses the reverse precursor coming from the end of the tube (lines Gx in Fig. 5). On the contrary, we observe in the recorded interferogram that the gradient region (zone "f" in Fig. 5) increases with time. Another point is that the main precursor is observed to slow down after crossing the reverse wave (at z=3.5mm). Slowdown of the precursor front after crossing with the reverse radiative precursor has been observed in other shots. As the mean opacity changed with temperature, the change of the optical

We numerically studied the shock 2D properties for different values of the lateral radiative losses. The boundary condition was of a constant piston velocity of 63 km/s, corresponding to the result of a MULTI 1D simulation of the whole target. Although the piston velocity is measured to be 30 km/s, the preheating of the gold back layer is equivalent to an increased piston velocity. MULTI simulations, including lateral radiative losses, yield similar precursor front with a 30 km/s velocity preheated piston or with a 63 km/s velocity cold piston. 2D results presented below suggest also that it is a good estimation. The 2D simulations are performed with the HERACLES hydrodynamic code [25], which includes M1 radiation transport, Super Transition Array opacity [26] and equation of state from OPA-CS hydrogenic model [27]. We report in Fig. 10 the computed and measured average transverse electron density in the precursor at two different times (20 and 40 ns) and for two values of the lateral radiative losses (20% and 40% of incident x-ray fluxes) at the gold walls of the tube. From this comparison we can infer a value of lateral losses around 35% (albedo=0.65).

As expected from the material albedo (albedo increases with the atomic number), this value is smaller than the value of 60% derived from earlier studies where the shock was propagating in a glass and aluminium tube [11], instead of a gold-coated tube in the present study. The computed gradient length L # of the precursor front presents a small time variation, in agreement with the observation of almost parallel fringes in the recorded interferogram between 20 ns and 40 ns (Fig. 10), after the precursor built up and before the upstream precursor crossing.

Figure 10 : transversally averaged electron density <N e (z,t)> at two times (20 ns in red and 40 ns in blue) : experimental values (circles) and electron densities computed with HERACLES for two values of the lateral radiative losses (dashes: 40 % , solid line: 20 % ).

Note that the simulation shows a quasi-constant gradient length.

We apply the filtering procedure to the interferogram from shot #1030_05

(displayed in Fig. 7) and derive the following plot of density profile (Fig. 11) for time between 10 ns and 40 ns after the laser pulse. In this shot, the shock tube was filled with a 0.17 bar, 50-50 Air-Xenon mixture. This shot exemplifies the split precursor with its plateau signature.

The precursor moves with a velocity of ~ 90 km/s and the density peak velocity is around 60 km/s. Precision is estimated around 5 10 17 cm -3 and 0.01 mm. Note that the density profiles in the density peaks drawn with dashes in Fig. 11, are indicative and cannot be measured from the interferogram with the interferometer setting we used. The dashed lines are drawn for guidance but lay in the V-shaped region where density cannot be measured.

-TRANSVERSE INTERFEROMETRY

Longitudinal interferometry gives information about the time variations of the averaged transverse electron density <N e (z,t)>, versus the direction z of shock propagation. It gives the longitudinal structure of the radiative precursor, and allows measure of the front velocity, but it does not give direct information about the 2D shock structure. To access it, we performed a transverse interferometric study with the same kind of target, turning the camera by 90°. Now, the slit of the streak camera images a transverse section of the shock tube at a distance z 0 from the initial position of the piston. Transverse interferometry traces time variations of the electron density <N e (x,t)>, averaged over the other transverse direction y, at a fixed distance z 0 .

For this study we used targets CF61 and CF59 with no gold coating but aluminium coating. The gas in the tube is then in contact with aluminium walls on two opposite sides and with aluminized glass windows for the two other sides. Actually, aluminium rapidly oxidizes into alumina (Al 2 O 3 ) and oxygen lines have been observed with the backside XUV spectrograph [START_REF] Stehle | Experimental study of radiative shocks at PALS facility[END_REF]16,17]. The section of the cell, 1.2 x 1.2 mm 2 , is larger than the nominal focal spot (~ 0.7 mm), therefore curvature of the shock front from pure geometrical reasons is expected in the beginning (~1mm) of the propagation. The tube length is again 6 mm. These targets are filled with Xenon at 0.1 bar.

The results are presented in Fig. 12 for two different values of the distance from the piston, z 0 =1.5±0.5 mm and z 0 =3.0±0.5 mm. In the latter case, the canal width was obscured by some misaligned mask, and only 1mm is visible, leaving a 0.2 mm obscure zone on the left of the interferogram (Fig. 12b), not noticed in preliminary results [START_REF] Stehle | Experimental study of radiative shocks at PALS facility[END_REF]. The horizontal axis corresponds to the transverse direction (1.2 mm) and the vertical axis to the time (100 ns).

Post mortem analysis of the targets shows that, in the first case (a), the laser pointing was very close from the lateral wall (approx. one half of the focal spot actually in front of the canal) and fully inside the canal section for the second (b), although shifter from center by 0.15 mm, as deduced from the interferogram. Laser energy in these two shots is ~150 J and ~170J. Probably because of a hiccup of the laser, the main pulse delay after the camera synchronizing pulse is 20 ns later on shot #1031_02 (Fig. 12b) than in shot #1101_03 (Fig. 12a). The small initial "collective" shift mentioned earlier can be used as a time fiducial of the main pulse. Note that a confirmed double pulse in another shot results in the same time delay. We have checked with hydrodynamic simulation that double pulse does not change the structure and velocity of the radiative shock launched in the Xenon, as a consequence of the launch by rocket effect. Only longer pulse and ramp shape would significantly change it. The positions of laser time arrivals are reported with black arrows, and the location of the focal spot is displayed above the interferograms. The lateral extension of the flat part (i.e. with same arrival time) of the shock section is around 200 microns at t=30 ns (Fig. 12b), and approximatively 400 microns at t=17ns (Fig. 12a) if we assume that the focal spot is centered on the edge of the canal.

As the width of the canal exceeds the shock section, the radiative losses are increased.

Moreover, lower piston velocity at the edges of the focal spot (because of lower laser intensity) -and beyond-is expected. As a consequence, a spherical shock behavior is expected until the first 1-1.5 mm distance of propagation before recovering a somehow planar structure by filling the full width of the canal. On the contrary, lateral radiative losses will cool down the shock temperature peak close to the walls and later on even create some curvature of the precursor and the shock itself [21]. 2D simulation is then required for full understanding of the front shapes.

Recorded interferograms (Fig. 12) show indeed lower shock front velocities far from the center of the focal spot, or more precisely, arrival of higher density and/or steep gradient appears later far from the center. The time delay $t between the precursor arrival at x=500 !m and x=0 from the focal spot center is measured to be $t ~ 10 ns (resp. $t ~ 5 ns) after a propagation distance of z 0 = 3 mm (resp. z 0 = 1.5 mm). On the other hand, the precursor foot, identified by the beginning of the fringe shift (shown as a straight white dashed line in Fig. 12), appears already planar (arriving at the same time on the whole width of the canal) for the two distances from piston we observed. Such a feature of a flat precursor foot ahead of a curved shock has been observed numerically with the 2D hydro-rad simulation by Leygnac et al, at least at early time, see Fig. 9 of ref. [START_REF] Leygnac | [END_REF]. They use a realistic laser intensity distribution in the focal spot, close to the one we have in our experiment, and a comparable transverse size of the channel.

The times of disappearance of the fringes at the center of the focal spot, and on the left of the canal in shot #1101_03, and at approx. 0.15 mm from the edge in shot #1101_02, are respectively ~13.5 ns and ~31 ns. However, distances from the piston are known with a poor accuracy, not better than 0.5 mm. This corresponds to an average velocity around 110±20 km/s and 95±20 km/s from 0 to resp. 15 ns and 35 ns. These value are compatible with the precursor velocity derived from longitudinal interferometry at these times of 15 ns and 35 ns, although we expected smaller values due to increased lateral losses.

We note also that in both records, the precursor foot, when the fringes start to shift, arrives at the same time in the whole width of the canal. Translated in terms of spatial shape, the precursor foot is already planar, though the precursor breakout, when the fringes disappear, shows largest delay in the wings of the focal spot, which translates into a spatially curved front. Using the same procedure than for "longitudinal" interferograms, we are able to derive the time evolution of the electronic density at this distance z 0 =3 mm from the piston, and at lateral distance x from the focal spot center between 0 and 0.6 mm. These time profiles are displayed in Fig. 13. The rise time are almost equal on the whole width, but with a larger delay far from center. Except for the very beginning which appears to arrive at the same time, as already mentioned, the time history for each distances from center are very close in shape, but with a variable delay increasing from center to edges. Translated in terms of propagation distances, this means that the precursor length is rather constant on the whole width of the tube, but that the precursor presents some curvature, again except for the very beginning of the precursor which is almost flat. Pure hydrodynamics tell that the shape of the hydrodynamic shock (i.e. the density jump) should be flat after propagation over a few diameter of the shock tube. However radiative losses through the walls have been demonstrated to create a curved precursor [11,21], in competition with the hydrodynamic flattening. 2D simulations are needed to discriminate between transverse variation of the piston velocity, spherical propagation, effect of lateral radiative losses and address competition between these effects.

-CONCLUSIONS

In this paper, we present comparison with 2D simulation of the recorded traces of a radiative precursor with an average front velocity around 85 km/s. Though there are puzzling questions remaining, measured electron density profiles at different times are in agreement with simulation. The results are consistent with radiative losses at the gold-coated walls of 35% (albedo of 0.65), expectedly less than the 60% for Al (albedo of 0.4) derived in the previous experiment [11]. Two other interesting features have been observed, a slowing down of the radiative precursor in pre-shocked gas (heated by an other, upstream, radiative wave), and a detached ionization wave or split precursor. In the shots we analyzed, the stationary regime has not been reached before the precursor crosses the reverse radiative wave coming from the other end, though we observe an almost stationary gradient length of the main ionization wave. On the contrary, we observed that the extension of the gradient region increases with time. Transverse analysis of the radiative precursor has also been done, and gives a precursor velocity in agreement with the velocity derived from the longitudinal analysis. Time history of electron density at various distances from the tube axis has been measured at 35-40 ns after the laser pulse. Further 2D simulations are required for full analysis.

-ACKNOWLEDGMENTS

The experimental campaign "PALS project#1077&1386" reported in this paper was carried We also acknowledge financial support from the OPTON Laser International Corporation.

Figure 2 -

 2 Figure 2 -schematic layout of targets for interferometry. Selection of the observation regions (hatched areas) is done by rotation of the streak camera and its entrance slit. All 4 sides can be aluminium or gold coated.

Figure 3 :

 3 Figure 3: Temperature and density profiles computed with the one-dimensional hydrodynamic code MULTI[18,[START_REF] Busquet | An Extended Version of the MULTI Code[END_REF]

Figure 4 :

 4 Figure 4:shot #1029_07 interferogram in longitudinal configuration for a target filled with Xenon at 0.1 bar. Raw image (a) and processed image (b) with back ground substraction. Additional FFT filtering is used in Fig.9. Time runs on vertical axis for 100 ns, distance z from the initial position of the piston runs on horizontal axis for 6 mm. Main shock goes from left to right. Superimposed lines identify the different time and space domains discussed in the text.

Figure 5 :

 5 Figure 5: full identification of zones and limits observed in Fig.4: zone a: electro-magnetic perturbation to the streak camera at early times; zone b: unperturbed space & time region; zones d,e,f,h: radiative precursor, precursor front is located on line A; zones g: reverse radiative precursor; zone e; splitting of radiative precursor; zone f: fully developed ionization wave; zone h: precursor slows down as it propagates in the plasma preheated by the upward ionization wave; zone c: shadow of the piston, we believe that the rear surface of the piston is located on line C, moving at a velocity around 30 km/s. All these features have been identified on other shots, with different laser and target conditions.

Fig. 6

 6 Fig.6 fringes positions (b) derived from schematic density profiles (a) at successive times with an ionization wave detaching from the initial precursor.

Fig. 7

 7 Fig.7 processed image of shot #1030_05 (50-50 Xenon/air mixture at 0.17 bar) also displays a split precursor signature (V-shaped flat fringe between 2 zones of parallel fringes with different slopes), and a backwards precursor coming from the bottom of the tube. Slow down of the main precursor after shock crossing is equally clearly seen.

Figure 8 :

 8 Figure 8: Synthetic interferogram (a) with simple modeling of 2D effects of the lateral losses[24], computed for 135 J laser energy on piston, and 0.1 J on back window (we found other combinations giving similar results). The exact shape will depend on 2D effects and on ionization value around 10 eV. As seen in inset, including a 0.3 J preheat in the gold back layer of the piston creates comma-shaped fringes as observed in zone "d" of experimental record.

Figure 11 :

 11 Figure 11: electron density profiles at different times after the laser pulse derived from the interferogram displayed in Fig.7. Precision is estimated around 5 10 17 -3 and 0.01 mm.

Figure 12 :

 12 Figure 12 : "transverse interferograms" of 1.2 mm wide canals at two different distances z 0 from the initial piston positions, approximatively 1.5 mm (a, shot #1101_03) and 3.0 mm (b, shot #1101_02). The field of view is reduced to ~ 1 mm width in (b). Time runs vertically for 100 ns (top to bottom) and transverse position runs horizontally for 1.2 mm. Laser time arrival is pointed with black arrows, at 13.5 ns (a) and 36 ns (b), while precursor foot is pointed with red arrows. The horizontal arrows on top of the interferograms correspond to the focal spot positions.

Figure 13 :

 13 Figure 13 : transverse interferometry at distance z=3mm (shot#1101_02): (a) processed zoomed interferogram and (b) time evolution of electronic density at different distances from center. Numbers on top of curves are distance from the focal spot center in units of 0.1 mm. Misalignment of some mask limit the visible part of the canal to 1 mm.

  out in 2007, involving Ouali Acef, Patrice Barroso, Michel Busquet, Norbert Champion, Chantal Stehlé (Observatoire de Paris), Guillaume Loisel, Frédéric Thais (CEA Saclay), Krzysztof Jakubzak, Michaela Kozlova, Tomas Mocek, Jiri Polan, Bedrich Rus (Department of X-Ray Lasers, Institute of Physics / PALS Center), under the P.I.ship of Chantal Stehlé and Michel Busquet in the framework of the LASERLAB facilities network [28]. The authors give a special thank to P.Barroso and O.Acef whose contributions were instrumental in the fabrication of the targets and in the design and assembly of the Mach-Zehnder interferometer. We thank O. Madouri (LPN) and V.Petitbon (IPN) for providing us with the SiC windows and the gold coated polystyrene thin films. We acknowledge financial supports from the Access to Research Infrastructures activity in the Sixth Framework Program of the EU (contract RII3-CT-2003-506350 LaserLab Europe), from the RTN JETSET (contract MRTN-CT-2004 005592), from the French National Program of Stellar Physics (PNPS) CNRS-PICS 4343. One of the authors (M.G.) acknowledges the financial support provided by the Spanish Ministry of Science and Innovation through the Juan de la Cierva grant. This research was partially supported by the Czech Ministry of Education, Youth and Sports (project LC528).

Shot Name Target Name Section shape Transverse size Length Walls coating Fill gas laser energy

	1029_07 CF7	square	0.7 mm	6 mm	gold	Xe, 0.1 bar	166 J
	1030_05 CF20	square	0.7 mm	6 mm	gold	50-50 Xe+Air,	173 J
						0.17 bar
	1101_02 CF61	square	1.2 mm	6 mm	Al 2 O 3	Xe, 0.1 bar	151 J
	1101_03 CF59	square	1.2 mm	6 mm	Al 2 O 3	Xe, 0.1 bar	169 J
	1029_08 CG32	circle	0.7 mm	2.8 mm Al 2 O 3	Xe, 0.1bar	168 J
	1029_04 CG35	circle	0.7 mm	2.8 mm Al 2 O 3	Xe, 0.1bar	170 J
	1030_06 CG50	circle	0.7 mm	2.8 mm gold	50-50 Xe+Air,	171 J
						0.17 bar

Table 1 :

 1 summary of the main characteristics of the different shots and targets.

properties of Xenon heated by the reverse wave is expected to modify the precursor front velocity.


Carlos Herrera
email: carlos.herrera@cran.uhp-nancy.fr

André Thomas
email: andre.thomas@cran.uhp-nancy.fr

Sana Belmokhtar
email: sana.belmokhtar@cran.uhp-nancy.fr

Rémi Pannequin
email: remi.pannequin@cran.uhp-nancy.fr

A Viable System Model for Product-Driven Systems ⋆

Keywords: Product-Driven Systems, Viable System Model, Manufacturing Planning and Control Systems, Flexibility, Adaptability

This paper describes a modeling approach for product-driven systems based on the Viable System Model (VSM). A general VSM description is presented, highlighting the pertinence of this approach for modeling intelligent product systems, specifically when a compromise between control and autonomy is aimed. An application is also provided for modeling a hybrid centralized/distributed production planning and control system. System modeling using the conceptual framework provided by VSM, allows to handle the complexity of the planning and control functions, considering aspects such as efficiency, flexibility, adaptability, scalability and reusability.

Introduction

The reduction of the Product Life Cycle caused by the ever growing demand for customization and global competitiveness, has imposed new challenges for many industrial sectors. These challenges force companies to organize and structure themselves, adapting their internal processes towards a high changeable environment and facing their own internal failures. In this context, centralized and hierarchical approaches applied to the decision making process, can be inadequate, especially under conditions of disruption and long-term changes [START_REF] Mařík | Industrial adoption of agent-based technologies[END_REF][START_REF] Mařík | Industrial applications of agent technologies[END_REF]. An alternative approach to this conventional hierarchical organization is the concept of Product-Driven System (PDS).

A PDS, changes the vision to a more interoperable and intelligent system, postulating the customized product as the controller of manufacturing enterprise resources [START_REF] Morel | Manufacturing plant control challenges and issues[END_REF]. This leads to the design of an intelligent product [START_REF] Meyer | Intelligent products: A survey[END_REF], which has been defined as an entity with a physical and information-based representation, able to influence decisions which concern itself [START_REF] Mcfarlane | Auto id systems and intelligent manufacturing control[END_REF]. From a practical perspective, Radio-Frequency Identification (RFID) has been widely accepted as a suitable technology linking information systems with the physical world [START_REF] Vrba | Using radio frequency identification in agent-based control systems for industrial applications[END_REF][START_REF] Thomas | Simulation for product-driven systems[END_REF].

Despite the increasing development of PDS [START_REF] Pannequin | The performance of product-driven manufacturing control: An emulationbased benchmarking study[END_REF][START_REF] Berger | Semi-heterarchical allocation and routing processes in fms control: A stigmergic approach[END_REF][START_REF] Blanc | A holonic approach for manufacturing execution system design: An industrial application[END_REF], currently, there is no specific modeling framework for this kind of systems. According to [START_REF] Morel | Manufacturing enterprise control and management system engineering: paradigms and open issues[END_REF], an important condition for these new approaches is to contribute to the understanding of endogenous variables like emergence and self-organization, in a wide-plant automation context. In accordance with this, the appearance of these variables cannot happen if the system is not seen as a whole. Consequently, a key issue is to develop sufficiently general holistic frameworks for modeling these multi-agent organizations, integrating the decision making process at the different levels. In this way, the model should allow the system to exhibit proprieties such as: flexibility, interoperability, robustness, scalability, reconfigurability and reusability.

Therefore, the proposed modeling approach is based on the conceptual and theoretical framework proposed by the Viable System Model (VSM). This model, since its origin in the fifties, as the result of the work of Stafford Beer, has been subject of a continuous validation and application until now. Some recent related works applying VSM concepts can be found in domains such as: production management [START_REF] Herrmann | Lean production system design from the perspective of the viable system model[END_REF][START_REF] Rosenkranz | Designing ic structures by variety engineering[END_REF], autonomous distributed systems [START_REF] Grishikashvili | IMPROMPTU: Software framework for self-healing middleware services[END_REF][START_REF] Ribeiro-Justo | Intelligent reconfiguration of dynamic distributed components[END_REF][START_REF] Thompson | Towards viable computer systems: a set theory interpretation of ecological dependence within beer's self-organizing viable system model[END_REF] or in modeling communities of autonomous agents [START_REF] Truszkowski | A cybernetic approach to the modeling of agent communities[END_REF]. This differs with the nonexistent utilization of VSM in the Intelligent Manufacturing Systems (IMS) approaches, considering its high similarities in terms of objectives and tackled problems.

The objective of this exploratory work is to describe the main concepts involved in VSM and how this model can be applied for modeling Product-Driven Systems. The high similarity in terms of objectives and topics, between VSM and the approaches arisen from the IMS initiative is also highlighted. As well, this paper presents an application to model a hybrid centralized/distributed Product-Driven Manufacturing Planning and Control System, focusing on how an intelligent product could be interpreted as a viable system. This paper is organized as follows: section 2 presents a basic but sufficient description of the main concepts involved in VSM necessary to develop the proposed modeling approach. Section 3 presents the approach focusing on the elementary object of the proposed structure that is the intelligent product and also describes an application of VSM to model a Product-Driven Manufacturing Planning and Control System. In section 4 a discussion of the main findings and facts is presented. Finally, section 5 briefly presents the conclusion.

The Viable System Model

As previously introduced, the Viable System Model (VSM) results from the research work of Stafford Beer [START_REF] Beer | Cybernetics and management[END_REF][START_REF] Beer | Decision and control[END_REF][START_REF] Beer | Brain of the firm: the Managerial cybernetics of organization[END_REF][START_REF] Beer | The viable system model: Its provenance, development, methodology and pathology[END_REF] in the domains of neurophysiology, cybernetics, operational research and social sciences. The origins of VSM date from the work of Beer applied to the steel industry in the fifties. This research can be placed in the line of works of Norbert Wiener, Warren McCulloch and Ross Ashby [START_REF] Espejo | The viable system model a briefing about organisational structure[END_REF]. The main objective of the model was to identify and to explain how systems are viable, in other words, how it is possible that some systems can maintain an independent existence [START_REF] Beer | The viable system model: Its provenance, development, methodology and pathology[END_REF].

Although VSM is a general model for the study of any viable system, the most concerned application area has been human activity organizations, i.e., corporations, firms or governments [START_REF] Beer | The liberty machine[END_REF][START_REF] Beer | Designing freedom[END_REF]. In this domain, VSM changes the view of the traditional management model based on command and control, in which a control system is designed as a pyramid and such decisions are disaggregated in a top-down manner at different structural levels. The main difference, inspired by the biological organization, consists in changing this hierarchy by a structural recursion.

The premise of this change of perspective was inspired from the living beings composition (molecules, cells, etc...). Indeed, they have properties of autonomy, auto-organization and auto-regulation, allowing them an independent existence. The differentiation of their functions and the relationships between these elementary components produce more complex systems, without that subsystems essential properties would be lost. Also, one of the most important properties of a viable system is recursion. Any viable system contains and is contained by another viable system. Every subsystem maintains its autonomy towards its environment, but it also contributes to generate the viable system in which it is included. In that way, a viable system and its different subsystems have the same structural requirements. Consequently, a viable system supports its objectives thanks to an overall cohesion and adapts itself by the autonomy of its subsystems.

Viable system model functions

VSM was developed looking for invariances in organic systems. These invariances allow to define a homomorphism of their functions, organization and structure. Beer defines five elementary functions that any viable system must have: implementation, coordination, control, intelligence and policy.

Implementation : this function refers to primary activities, which produce products or services that materialize the identity of the system [START_REF] Espejo | The Viable Systems Model -Interpretations and Applications of Stafford Beer's VSM[END_REF]. These activities add value to products and are identified after an analysis of what the system does. Besides, in a viable system primary activities can support a functional differentiation.

Coordination : this coordination function (anti-oscillatory) corresponds to the coordination among primary activities. In a viable system, this coordination is not necessarily accomplished in a top-down manner like a hierarchic management system. Indeed, primary activities can be coordinated in a centralized or distributed way thanks to cooperation and information exchanges.

Control : in a viable system, control refers to the function which regulates and ensures the auto-organization of the system. This is due to coordination and monitoring functions. Monitoring function (or sporadic audit function) allows at the same time to evaluate the actions of primary activities and to hold the coherence of the global activity (all primary activities). Notice that, control function is the function that defines the control/autonomy degree of the actions accomplished by the primary activities.

Intelligence : the intelligence function is responsible for system adaptability. This function is the link between primary activities and their environment. To achieve this adaptation, the intelligence function must be capable of treating the information which comes from the environment, with the objective to anticipate perturbations. Besides, this function is responsible of the coherence between local and overall system objectives.

Policy : the policy function keeps the system objectives at the different recursive levels.

Variety and recursion

The variety of a system is defined as all possible system states and it can be used as a complexity measure. In this way, a controller will be effective if it is capable of attaining at least the same number of states as those which it wants to control. This was expressed by Ashby [START_REF] Ashby | An introduction to cybernetics[END_REF] in the law of requisite variety.

"A controller has requisite variety -that is, has the capacity to maintain the outcomes of a situation within a target set of desirable states -if and only if it has the capacity to produce responses to all those disturbances that are likely to take the outcomes out of the target set".

To do that, a viable system tries to reduce the variety coming from the environment and to amplify the variety of its control function to reach a balance (homeostasis). The variety that system is not capable to control (residual variety), should be absorbed with the objective to ensure viability. Notice that if the system is not capable to control residual variety, it can lead to the loss of the systems identity.

Thus, control (management) is composed of three functions: policy, intelligence and control. The relationships between these functions show that the feedback between intelligence and control functions must take into account the objectives of the system at its recursion level. The coordination and monitoring functions correspond to the information flow which allow reduction and amplification of variety respectively. Furthermore, the viable system object of control, is the part of the system where primary activities will take place . This viable system can be decomposed in other viable systems at lower complexity levels. Figure 1 shows an example of a decomposition of a viable system in three subsystems. The property of recursion of VSM allows continuing this recursive process until the required level of detail. In the example presented in Figure 1, it is possible to break down each of the three viable systems in new viable sub-systems. Also, the whole system can be considered as a subsystem of another viable system at an upper recursive level. Thus, for example, a football player can be seen like a viable system. In this case the respiratory or circulatory systems are viable subsystems of the whole "football player viable system". These viable subsystems can be then decomposed in other viable subsystems as the cardiovascular or lymphatic systems for the circulatory subsystem, and so on. On the other hand, the "football player viable system" can be also viewed as a subsystem belonging to a bigger viable system that could be the football team.

3 Product-driven systems based on VSM

An intelligent product as a viable system

As it was expressed before, a viable system is designed focusing attention on the primary activities, i.e., the system components which complete work tasks. A conventional recursive decomposition of a production system, Fig. 1. The Viable Systems Model will decompose the system, for example, on the shop-floor, production cells, production lines and machines [START_REF] Gou | Holonic manufacturing scheduling: architecture, cooperation mechanism, and implementation[END_REF]. In that case, machines would be the atomic entities of the system at the lowest recursion level.

In contrast with this conventional interpretation, we consider the product to be the elementary decision-making entity responsible for driving work tasks. Therefore, it is considered as the basic element of the production process and it is designed as a viable system. Others system entities such as machines, conveyors, automated guided vehicles, team workers, etc., are then considered in the environment. These entities interact with the product only in terms of events leading to lack of availability, disruptions, constraints, etc. Figure 2 shows the intelligent product structure which is proposed.

Fig. 2. The Intelligent Product as a Viable System

As it has been said in the introduction, the intelligent product is defined as an entity able of interacting and communicating with its environment. When this physical entity transits on the shop-floor, it will be able to recover information concerning both its own state and the system state. Then, focusing on the product, all the production planning system can be structured from the information recovered by this intelligent product. Also, decision-making problems are addressed to their corresponding aggregation level. This approach quite differs from the conventional holonic approach, in which products and resources are considered to be active entities [START_REF] Van Brussel | Reference architecture for holonic manufacturing systems: PROSA[END_REF]. The choice to not consider resources as belonging to decision-making entities, is voluntary made to express the central role played by the product in the decision that concern it. However, it is necessary to point out that VSM allows a multi-functionality of activities, like in living system. The primary activities of the intelligent product are data collection and interaction functions. The data collection activity is designed as the action which allows the product to get information from other products and to give information to them. On the other hand, interaction functions allow products to interact with their environment, for example by using actuators. Table 1 describes the components of the intelligent product. Notice that product is designed with both, an informational and a physical part (as a holon). Then, at the different states of its life cycle, this product will activate these two parts according to its state in the system. Before beginning its manufacturing process this product has activated only its informational part (an active agent). Then, once it begins its manufacturing process, it should activate in addition to the informational part the physical one.

In this way, the product informational part will always be active. This informational part, lives in one or several computers, allowing it to communicate with others agents to make decisions in a cooperative way. An alternative is to load the informational part into the physical part, but its feasibility will depend on the characteristics of the manufacturing process. Notice that an intelligent product designed in this manner, belongs in the category of cognitive agents, rather than reactive agents.

Application for production planning and control

A Manufacturing Planning and Control System (MPCS) contains in general five main activities, these are Strategic Plan, Sales and Operation Planning (S&OP), Master Production Schedule (MPS), Scheduling and Execution. Each of these activities (plans), proposes decisions for different planning horizons. Commonly, decisions are taken using a rolling horizon, i.e., plans are recomputed with a certain frequency. In this way, strategic plan can be reviewed biannually or yearly, S&OP monthly, MPS every week, Scheduling daily and Execution in micro-periods of hours or minutes. Each of these activities makes decisions based at some level of product aggregation which can be product families, manufacturing orders, lots, finished products and components [START_REF] Vollman | Manufacturing Planning and Control Systems[END_REF].

In this context, one of the main problems is to adjust decisions taken at the different levels. When internal or external disturbances occur, objectives at different levels are hardly fulfilled. Some of the most common disturbances are demand changes (external) and production capacity variations (commonly due to machine breakdowns). Then, frequent decision changes lead to a considerable system instability [START_REF] Herrera | Simulation of less master production schedule nervousness model[END_REF], which deteriorates both efficiency and productivity.

While at planning horizons of long and medium terms, changes are less frequent, in short-term horizons they are more recurrent which strongly degrade the system performance. In this context, a MPCS system must give enough flexibility at operational levels to allow adaptation to disturbances, but also, to ensure coherence with the objectives defined at the others levels.

Specifically, the proposed application tackles the problems of MPS and Lot Streaming. The MPS consists of defining the quantities to produce for each item (products), for a planning horizon (generally three or four months), considering weekly demand, costs and capacity of the system [START_REF] Pochet | Production planning by mixed integer programming[END_REF]. This problem is generally modeled like a capacitated lot-sizing problem (CLSP). Once quantities are obtained, these quantities must be subdivided into sub-lots, and also sequenced, to be launched in the different production stages, that corresponds to the Lot Streaming Problem [START_REF] Sarin | Flow Shop Lot Streaming[END_REF]. In this way, it is possible to optimize the production flow reducing the weekly production makespan. Disturbances as changes of demand or machine breakdowns lead to the planning defined at the beginning of the week, already is no more valid, and consequently it is necessary to achieve adjustments towards the new conditions.

Therefore, the example application presented here, corresponds to a hybrid centralized/distributed system, which has for objective a self-adaptation face to internal and external disturbances. This system is based on a product holarchy, such that every decision level has a relationship with its product aggregation level. Regarding to the intelligent product introduced previously, the different levels are defined as holon communities, which have for objective to collaborate while assess and adapt decisions. The informational/physical nature of the system, added to the concept of structural recursion, lead quite naturally to the notion of holarchy. In a recent work [START_REF] Mella | The Holonic Revolution Holons, Holarchies and Holonic Networks[END_REF], the author defines VSM as a holon organization. More precisely, this holonic organization is defined as a cognitive holarchy composed by sub-holons modeled such that viable systems. Then, we design this hybrid MPCS system such a cognitive holarchy modeled as a Viable System. This holarchy is composed of different product aggregation levels also modeled as viable systems. Figure 3 shows the different aggregation levels proposed. Therefore, at each level entities such products, lots, manufacturing orders and family, represent agents modeled as viable systems. All these levels are updated using the information provided by the lowest level (products). Notice that, at every aggregation level, it is possible to identify one or several decision-making problems. In this manner, control is based on the adaptation of decisions at each level.

The objective is to react to external variations (like demand changes), in a centralized way and in a decentralized way for internal perturbations (like capacity changes). For internal perturbations, if it is not possible to find an alternative solution at the corresponding level, the problem rises to the next upper level (bottom-up process) and so on. For external perturbations, central system modifies global targets causing an adjustment (top-down) of lower-level decisions and defining new realizable targets at each level. While bottom-up adaptation process (right side in figure 3) has a cooperative character, top-down adjustment process (left side in figure 3) have a mandatory nature.

Figure 4 shows the viable system model of the hybrid MPCS system proposed. Notice first, that the higher level deals with the family product corresponding to the classical S&OP decision level. This suggest that the approach allows to consider all product families or upper product aggregation levels also.

Figure 4 presents all the components of the proposed hybrid system. Product holons (1) have the structure presented in figure 2, and are presented here as black points. In the same way, all recursive levels have the same structure, and for each one, all management functions must be viewed as control, intelligence and policy functions. At the upper level, the environment allows to obtain demand forecast, cost, and also, constraints arising from market and norms. An interesting point is the link with the Customer Relationship Management (CRM) activities of the company. [START_REF] Morel | Manufacturing enterprise control and management system engineering: paradigms and open issues[END_REF] shows that manufacturing order agents can eventually recover information from the environment. In this application, product agents update their information by a RFID system [START_REF] Morel | Manufacturing plant control challenges and issues[END_REF]. As said before, the proposed system is composed of four recursion levels, product, lot, manufacturing order and family. The whole decision system (MPCS) will be elaborated by the sum of all control, intelligence and policy functions relatives to all levels. Notice that, the combinatorial nature of the decision-making problems and the variability of the parameters (demand, capacity, etc.) do not allow an on-line re-computation of the plans once perturbations arrive. To cope with this weakness, the centralized decision about manufacturing orders quantities (lot sizing problem), is computed with a parametric approach. This method provides a set of alternative solutions according to the chosen parameters [START_REF] Herrera | Simulation of less master production schedule nervousness model[END_REF]. Tables 1,2,3 and 4 describe briefly the functions at each level. The physical part of this component, dispatch information relative to its state and the state of the system using RFID technology. The relationship between physical and informational parts (agent) of the product is one-to-many. Also, the physical part of the product agent evaluates and decides to cut or to continue production of a lot once perturbations level exceeds a threshold. 3 It corresponds to the information flow between lot agents.

4

The coordination function at this level refers to the communication protocol among product agents.

5

This function updates lot production time from product on-line data.

6

The control function implements a distributed algorithm to exchange products with others lot agents.

7

The intelligence function evaluates adaptation changes.

8

Policy function at this level ensures minimal and maximum sub-lot sizes, manufacturing order quantity and number of available lots.

Discussion

The relationship between hierarchy and heterarchy has been widely studied by VSM. In fact, VSM cope with this in terms of degree of control/autonomy implemented in all control functions. The monitoring function is These agents guide a local search procedure to find near optimal symmetric solutions using parametric information provided by the central level.

10 It corresponds to the information flow between manufacturing orders agents.

11

The coordination informs about search results.

12

The monitoring function at this level can trigger a replanning of weekly production quantities.

13

Local search function computes near optimal feasible solutions (plans) according to parametric alternatives and the system state.

14

The intelligence function maintains updated the information about real production time of each manufacturing order.

15

The policy function provides information about current manufacturing order quantities. The intelligence function uses forecasts to estimate parameters like demand or cost. Demand can also be adjusted considering Customer Relationship Management (CRM) functions, including changes and proposals.

21

The policy function keeps the system performance in terms of costs and stability.

expressly defined with the intention of auditing the functioning of primary activities (agents) and not to control as in conventional system of command and control.

Another concern in the origins of VSM has been adaptability. As it was described in the previous section, VSM was developed with the objective to understand the mechanisms which allow biological organisms to survive to changes in the environment. A viable system is designed to self-adaptation in a changing environment, by the implementation of the necessary mechanisms to support its viability. Here, it is not possible to identify a specific function which ensures adaptability, since the whole system is defined to fulfill this objective, thanks to its different elementary functions. This characteristic of adaptability is also one of the main objectives of the paradigms arising from IMS initiative.

Moreover, one of the basic properties of the viable systems is scalability because these systems are structurally recursive. This notion of recursion has been mainly exploited by bionics manufacturing systems, which make an analogy from biological organisms. These are composed of atoms, molecules, cells, membranes, organs, systems and finally organisms. This notion has been also exploited by fractal manufacturing systems which show clear properties of recursion and auto-similarity. The last property of auto-similarity of fractal systems is also included in the viable systems through its property of structural recursion. In that way, a viable system will keep the same structural requirements at any complexity level. These concepts have a direct relationship with reusability, which is another objective of IMS systems. These three points about autonomy, adaptability and scalability highlight the strong relationship between IMS approaches and VSM objectives.

On the other hand, an important shortcoming of conventional centralized/distributed approaches, i.e., MPCS systems using MRP II based planning system and lean manufacturing techniques (kanban method) to production control, concern the lack of flexibility in the decision making process. According to APICS, flexibility can be defined as the ability of the manufacturing system to respond quickly, in terms of range and time, to external or internal changes. Flexibility can be reached, to absorb disturbances and ensure feasibility of plans, introducing some involvement of operators in the decision process. Since decisions could not wait until recomputing, decentralized (local) decisions are usually taken without any guarantee of global performance. Consequently, the predictive planning is used as a reference planning where deviations happen frequently. Several possibilities could be adopted, although only few of them will be able to maintain an acceptable global cost. In this context a system such the one proposed, can be useful maintaining a coherence with the global objectives and give the needed flexibility at the operational level.

Finally a hybrid centralized/distributed manufacturing control system can be seen like a viable system if the designers of such systems are able to ensure recursive characteristics. That is to say that each decision level include the lower ones. To be realistic this kind of concept induces real time closed loop systems. This last point could be seen as a limitation according to the available currently technology. But the last improvements made in the field of Auto-ID technologies lead us to think that we will be probably able to implement such systems soon.

Conclusion

In this paper, we have presented the main concepts involved in the VSM. Also, it has been possible to identify several common points between IMS approaches and VSM objectives. Moreover, we have presented an application of the proposed modeling framework to model a MPCS product-driven system. The main advantage of this application is to reach a coherence among the different decision levels giving a high degree of flexibility to the system. The proposed modeling approach and product-driven systems can be adapted to be used in different industrial applications.

Fig. 3 .

 3 Fig. 3. Agent communities for planning and control

Fig. 4 .

 4 Fig. 4. The hybrid MPCS system

19

  Control function at this level has three sub-functions: evaluation, PMPS and lot streaming. (a) Evaluation function assesses the global performance of the system in terms of efficiency, stability and feasibility. (b) The PMPS function (Parametric Master Production Schedule) gives alternatives of quantities to produce for the period. To do that, a parametric lot-sizing model gives several solutions considering the trade-off between cost and instability according to the production capacity variation. This function is modeled as a Parametric Mixed Integer Programming (MIP) model, computed off-line once information about the next period has been validated.c) Lot streaming function computes a lot streaming MIP model to obtain initial values for lots and its sequence.

20

 20

Table 1

 1 Intelligent product components description.

	Function	Description
	Primary activities Input/output data (data collection)
		Environment interaction activities (actuators)
	Coordination	Communication between data collection and interaction activities.
	Control	Internal activity regulation by coordination and monitoring.
		Auto-organization and evaluation
		Cooperative algorithm (interaction with others products)
	Monitoring	Sporadic audit of the primary activities actions
	Intelligence	Internal and external knowledge, future anticipation, response actions
	Policy	Local goals and global constraints

Table 3

 3

	Lot level description
	Level Component Description
	Lot	2	A lot agent is composed of a variable quantity of product agents. Lot agents cooperate
			to adjust size and sequence changes induced by product agents.

Table 5

 5

	Weekly production level description
	Level	Component Description
	System	16	This agent represents the higher component level including all the other levels.
			Specifically, this agent represents all activities implemented by the proposed appli-
			cation.
		17	In this particular application, this level is implemented in centralized way. Then,
			the coordination informs changes of each manufacturing order quantity.
		18	This function updates manufacturing order quantities information.

Acknowledgments

The authors gratefully acknowledge the financial support of the CPER 2007-2013 Structuration du Pôle de Compétitivité Fibres Grand'Est (Competitiveness Fibre Cluster), through local (Conseil Général des Vosges), regional (Région Lorraine), national (DRRT and FNADT) and European (FEDER) funds.