Magari

Francesca Masini

Paola Pietrandrea

Keywords: non factuality, focus particle, construction grammar, discourse configuration, topology, lists

We propose a constructionist approach to the polyfunctionality of the Italian focus particle magari (roughly corresponding to 'maybe', but also 'I wish'). The sheer syntactic versatility of this word leads us to detect its formal regularities at the level of discourse configurations. This level of analysis, identified within the French linguistic tradition, is defined by the maintenance of a predicate-argument-adjunct structure in discourse. The salient feature of discourse configurations is their shape, which can be described by referring to a number of topological patterns: lists of elements in the same syntactic position, repetition of syntactic structures, shifting of elements from a post-verbal to a pre-verbal position and so on. These topological patterns are meaningful to an extent and they are eligible to be regarded as constructions.

Magari is shown to be regularly associated with a general topological pattern, namely a list of items that occupy the same syntactic position as the item focused by magari. Each semantic function of magari correlates with one particular kind of list. These associations of a form (the different types of lists) and a meaning (the functions of magari) are shown to be related to one another by means of inheritance links.

The polyfunctionality of magari

The word magari has attracted considerable attention among Italian linguists because of its especially intriguing polyfunctionality that knows no parallel in its counterparts in other European languages (cf. [START_REF] Arcaini | Le connecteur magari dans une perspective comparative[END_REF][START_REF] Arcaini | Italiano e francese. Un'analisi comparativa[END_REF][START_REF] Licari | Pour une analyse contrastive des connecteurs pragmatiques italiens et français: magari/peut-être, anzi/au contraire[END_REF][START_REF] Schiemann | La polisemia di magari (e forse). Analisi corpus based su C-ORAL-ROM italiano[END_REF]).

Firstly, magari can have the function of a general marker of non factuality. In this case, it roughly corresponds to the English adverb 'maybe'. See example (1):

(1) Magari è a casa 'Maybe (s)he is at home' Magari can also function as a scalar operator (in the sense of Fillmore, [START_REF] Kay | [END_REF][START_REF] Fillmore | Regularity and Idiomaticity in Grammatical Constructions: the Case of Let Alone[END_REF][START_REF] Kay | [END_REF], triggering a scale of non factuality whose extreme position is occupied by the constituent in the focus of magari. See (2):

(2) Bisognerebbe negoziare una tregua, un armistizio, magari la pace 'It would be necessary to negotiate a ceasefire, an armistice and maybe peace'

Besides, magari may act as a non factual concessive marker, as in (3), where the speaker concedes that the subject is clever despite thinking that he has not studied enough:

(3) Magari è intelligente, ma non è abbastanza preparato 'He might be clever, but he has not studied enough'

In imperatival contexts, magari weakens the illocutionary force of the order, as in the following example:

(4) Magari parlagliene tu! 'Perhaps you yourself could talk to him about it!'

Finally, magari functions as an optative marker. This happens when it occurs in exclamative contexts:

(5) Vorrei tanto vedere un film come quello. Magari ne facessero ancora! 'I really would like to watch a movie like that. I wish they still made some!' (6) A: Vuoi un po' di riposo?

'Would you like to rest a bit?' B: Magari! 'I'd love to! / I wish I could!'

The problem

The problem that arises is: how can we account for the polyfunctionality of magari? First of all, one should decide whether the functions of magari are somewhat related to each other or are completely independent, i.e. homonymous. There is a good reason for rejecting the latter hypothesis, namely: the set of functions held by magari-non factual, scalar non factual, non factual concessive, imperative, optative-recalls in most respects the semantic network developed by several irrealis markers of non factuality in various non-European languages (cf., e.g., [START_REF] Elliott | Realis and Irrealis: Forms and Concepts of the Grammaticalization of Reality[END_REF][START_REF] Gilbert | L'expression de l'irréel: essai de typologie[END_REF]. The crosslinguistic presence of similar semantic networks makes it fairly unlikely that we are dealing with pure homonymy. We therefore consider the various functions of magari as microsenses of this word, that is "distinct sense units […] that occur in different contexts and whose default construals stand in a relation of mutual incompatibility at the same hierarchical level" (Croft and Cruse 2004: 126-7). Under this perspective, the word magari has a hyperonymic reading and a cluster of hyponymous readings, whose default construals are sister incompatibles (Croft and Cruse 2004: 127).

The question now arises of identifying the contexts that licence the various functions of magari and the nature of the relations holding between these functions. Such a task is made more complicated by the sheer syntactic versatility of magari. Indeed the contexts in which magari occurs can be properly detected only by adopting a wide-ranging notion of context. In section 3 we describe the practical difficulties encountered in the analysis of magari and the theoretical approach and tools adopted for solving them, whereas in section 4 we provide a qualitative and quantitative description of magari and its various functions. In section 5, we give a construction grammar account of our findings.

The theoretical approach

Construction grammar

A fruitful theoretical approach to the kind of problem outlined in the previous section is to place the analysis of magari in the wide framework of construction grammar. As is well known, construction grammar comprises a number of different models (cf., among others, Croft 2001; Fillmore, [START_REF] Fillmore | Regularity and Idiomaticity in Grammatical Constructions: the Case of Let Alone[END_REF][START_REF] Goldberg | Constructions. A Construction Grammar Approach to Argument Structures[END_REF][START_REF] Goldberg | Constructions. A Construction Grammar Approach to Argument Structures[END_REF][START_REF] Kay | Grammatical Constructions and Linguistic Generalizations: the What's X doing Y? construction[END_REF], which nevertheless share a set of basic tenets. The main tenet regards the very notion of "construction", which is defined as a conventionalized association of a form and a meaning and is considered the basic unit of linguistic analysis. This definition virtually captures every meaningful unit of language, ranging from simple words to more complex and abstract sentence-level structures, such as argument structure constructions [START_REF] Goldberg | Constructions. A Construction Grammar Approach to Argument Structures[END_REF] or sentence types [START_REF] Michaelis | Towards a Construction-Based Theory of Language Function: the Case of Nominal Extraposition[END_REF]. It is thus clear that certain higher-level abstract patterns, those that are commonly considered as "context" for lower-level lexically specified units, may be treated as full linguistic objects in this framework, provided that they prove to be meaningful to some extent.

Another assumption of constructionist approaches that is crucial for our purposes is that they take into account "not only syntactic and semantic information, but also lexical and/or pragmatic information" (Kay 1990: 61) and that all this information is coded simultaneously in the construction and contributes to characterize the constructions itself.

This provides the tools for the detection of the correlations between certain contexts, or rather "constructions", and the various functions of magari. This latter theoretical issue has been recently addressed by [START_REF] Fried | Constructing Grammatical Meaning. Isomorphism and Polysemy in Czech Reflexivization[END_REF], who has convincingly argued that the relations between the different functions of the same polyfunctional lexical unit are better understood if one takes into account the entire construction in which they occur, rather than the single item under examination. Therefore, the entire construction becomes the true linguistic form to be investigated.

Still another aspect of constructionist approaches-and in particular of Goldberg's "cognitive construction grammar" [START_REF] Goldberg | Constructions. A Construction Grammar Approach to Argument Structures[END_REF])-that will prove useful in our analysis is the use of inheritance links, which account for the relations holding among constructions. The inheritance system works this way: if construction A shares some formal properties with construction B, then construction A also shares some semantic properties with B, and the two constructions are related by an inheritance link. As is well known, according to Goldberg (1995: 75ff), there are four major types of inheritance links: polysemy links (I P ), subpart links (I S ), instance links (I I ) and finally metaphorical extension links (I M ). 1 Given this framework, all the possible abstract constructions that host the adverb magari can be regarded as constructions that share at least one formal property-namely the presence of magari-and that are eligible to be linked to one another at the representational level. Therefore, once we have identified the form of the constructions in which magari occurs, we will have to determine which kind of inheritance links connect these various constructions to one another. First of all, though, we have to address the formal analysis of the contexts of magari, which is not unproblematic.

A practical difficulty

A practical difficulty in the formal analysis of magari concerns the above-mentioned syntactic versatility of this word, which makes it particularly hard to define its contexts of occurrence. Indeed, magari occurs in every illocutionary act: assertions (cf. examples (1) to (3)), orders (4), exclamations (5). It can also occur in questions, as exemplified in (7): 2 (7) Non potrebbe essere uscito con un amico? Non sarà magari con suo fratello? 'Don't you think he might have gone out with a friend? Couldn't he be with his brother?'

What is more, the categorial status of magari is not easy to define: it can be used either as an interjection (6) or as an adverb (cf. examples (1) through ( 5) and ( 7)). Occasionally, and retaining some of the semantic properties of its adverbial function, it can also be understood as a clause connective, as exemplified in (8):

(8) Magari un po' debolina, magari me la sono immaginata, magari è solo un effetto ottico… Ma vi giuro che l'ho vista [Web] 'Maybe a bit feeble, maybe I dreamt it, maybe it's just an optical effect, but I swear I saw it' As an adverb, magari can have scope on units of different size and category. First, it can have both a clausal scope, as in (1), (3), (4) and ( 5), and a phrasal scope, as in examples (2), ( 7) and ( 9) to (11):

(9) È un piacere venir qui e vedere tutta questa gente che si commuove per me e che magari ha pianto per la mia vittoria [Web] 'It's nice to come here and see all these people who are moved because of me and who, maybe, cried for my victory' (10) Gli aerei piccoli e molto utilizzati, con personale poco pagato e magari stanco, non possono dare la massima tranquillità né agli utenti né ai sindacati [Web] 'Small and thoroughly exploited aircrafts, with a badly paid and possibly tired staff, cannot fully reassure either users or trade unions' (11) Si discute magari male, ma sempre molto a lungo 'We discuss perhaps badly, but always at great length'

When magari has scope on a phrase, the latter can be a verb phrase (9), an adjectival phrase (10), an adverbial phrase (11), a prepositional phrase (7) and even a noun phrase as in (2). Besides, magari is endowed with an almost unrestrained syntactic mobility: it can occur in fact at every major phrasal boundary. For example, if we consider the proposition in ( 12), we may have the patterns in ( 13):

(12) Luigi è venuto 'Luigi has come' (13) a. Magari Luigi è venuto b. Luigi magari è venuto c. Luigi è venuto, magari
Some regularities can be easily detected even in such a complex picture. For example, magari's use as an optative is preferably expressed with an interjection in exclamative contexts. The imperative use is associated with orders.

Nevertheless, some difficulties remain in detecting the relevant context associated with non factual, scalar and concessive uses of magari. The assertive context, for example, appears to be associated with all these functions. The size and category of the unit within the scope of magari is not a relevant factor in determining the function of this word. As a matter of example, we have shown above that magari retains the same scalar function whether it has scope on a verb phrase (9), an adjectival phrase (10) or a nominal phrase (2). Such a function is also compatible with a clausal scope of magari, as shown in ( 14): ( 14) Forse è venuto ieri, ha passato qui tutto il pomeriggio e magari si è fermato a dormire 'Perhaps he came yesterday, he spent the whole afternoon here and possibly he stopped for the night'

Not even the distribution of magari within the clause seems to be a relevant parameter to detect its correct function. For instance, when it has a sentential scope, magari may have the same concessive function whether it fronts the clause (15), is pre-verbal (16) or, finally, post-verbal ( 17):

(15) Magari Luigi ha sbagliato, ma io non me ne sono accorta 'Luigi might have made a mistake, but I couldn't spot it' (16) Luigi magari ha sbagliato, ma io non me ne sono accorta (17) Luigi ha sbagliato, magari, ma io non me ne sono accorta This syntactic versatility of magari makes it not trivial to identify the structural constraints that characterize the maximally abstract magari construction (the "hyperonymic" magari) and all other subconstructions. As things stand, we could simply propose that, in all its functions, magari can be described as the only lexically specified part of a maximally abstract construction in which the only relevant information regards the internal make-up, i.e. the presence of the unit magari with its phonetic properties (even the information about its categorial status is underspecified, since it may behave both as an adverb and as an interjection). Such a characterization is obviously largely unsatisfactory for our purposes.

3.3.

Theoretical tools: discourse configurations, topological structures, topological patterns

The difficulty described in the previous section has led us to look for tools that could help in better defining the trans-categorial and trans-level nature of magari. Within the French linguistic tradition, a level of analysis has been identified that is called configuration de discours ('discourse configuration') (cf., among others, [START_REF] Blanche-Benveniste | Répétitions de lexique et glissement vers la gauche[END_REF], 1997;[START_REF] Blanche-Benveniste | Des grilles pour le français parlé[END_REF][START_REF] Kay | [END_REF]Gerdes and Kahane in prep.). A given predicate-argument-adjunct structure can also be instantiated more than once in discourse. For example, the spoken sequence in (21) features two repetitions of the ADJ 1 -ARG 1 -PRE-ARG 2 structure, beside the multiple instantiations of the ARG 1 and ARG 2 positions:

(21) praticamente per ogni tipo di gioco c'era un edificio specifico.

Per esempio il circo serviva alle corse dei carri, l'anfiteatro alle lotte dei gladiatori, lo stadio per i giochi atletici 'In practice, for every kind of game there was a specific building. For example the circus was for the chariot races, the amphitheatre for the gladiator fights, the stadium for athletic games ' [from Bonvino 2005: 61] The chunk made up of the sequence of units "that instantiate or repeat a given predicate-argument-adjunct structure" is called discourse configuration (Pietrandrea 2008a).

As this definition makes clear, discourse configurations are objects defined in purely syntactic terms. Interestingly, though, they may have a semantic investment. Let us consider the following example:

(22) Io mangio. Il mondo crolla 'I eat. The world collapses'

In this case there is a discourse configuration defined by one repetition of the syntactic structure ARG-PRE. The two sentences making up the discourse configuration depict totally unrelated situations. Still, the syntactic parallelism between the two sentences forces the addressee to find a semantic relation between them: in this case a relation of contrast. Interestingly, when the same situations are depicted by two contiguous but distinct structures, which hence do not form a proper discourse configuration, the addressee is not invited to postulate a relation between the two situations:

(23) ?? Sono io che mangio. Il mondo crolla ?? 'It is me who eat. The world collapses'

Discourse configurations can be more or less extended: while the discourse configurations in ( 19) and ( 20) are limited to a clause, the discourse configuration in (21) spans an entire text. Therefore, crucially, discourse configurations are defined regardless of the boundary between the clausal and the supraclausal level.

The discourse configurations from ( 19) through (25) are represented in "grids", i.e., through a rewriting procedure elaborated mainly by Blanche-Benveniste and colleagues (1979), [START_REF] Bilger | Contribution à l'analyse en grille[END_REF], Blanche-Benveniste and colleagues (1990), [START_REF] Bilger | Contribution à l'analyse en grille[END_REF]colleagues (1997), and[START_REF] Bonvino | Le sujet postverbal. Une étude sur l'italien parlé[END_REF] and Pietrandrea (2008a) for Italian. This rewriting procedure consists in a representation of the speech flow on a bi-dimensional plane and is constrained by three rules: (i) the horizontal axis of the plane should feature the sequence of the positions that define the predicate-argument-adjunct structure; (ii) the vertical axis should list all the actual realizations within each position; (iii) a left-to-right and top-down reading of the string contained in the grid should render the linear order of the represented chunk.

This representation highlights an important fact, namely that the salient feature of discourse configurations is their shape and not the categories they are made up of. We refer to the shape of a discourse configuration with the term "topological structure". Such a topological structure can be described by referring to a number of bi-dimensional "topological patterns": lists of elements in the same position, repetitions of syntactic structures, chiasms of elements shifting from a pre-verbal to a post-verbal position (or viceversa) and so on. 4 It should be noted that units belonging to different levels and categories may enter the same topological structure. For example, the two discourse configurations used as answers in ( 24) and ( 25) are made up of clauses and nominal constituents respectively. Nevertheless, they present the very same topological structure, characterized by a list of instantiations of the rightmost position, whose last element is preceded by magari (cf. section 4.4 for more details on this structure).

(24) A: Come mai è così tranquillo?

'Why is he so calm?' B: Sarà rientrato presto, si sarà riposato, magari avrà dormito 'He probably came back home early, rested, maybe slept' The body of research carried out on discourse configurations has shown, albeit incidentally, that certain topological patterns, as well as the various topological structures within which those patterns are unified, may have very abstract meanings. For example, we have seen above in ( 22) that the repetition of the same syntactic structure may carry a meaning of contrast (see also Blanche Benveniste 1997: 113). Another example of "meaningful" topological pattern comes from the listing of elements in only one position of the grid. The abstract topological pattern "list" has the very general meaning of "relation among the conjuncts" and may assume more specific meanings according to the exact way in which it is instantiated. For instance, it is acknowledged that a list instantiated by conjuncts preceded by one or more additive particles, is interpreted as an additive list (26).

(26) Ha comprato il pane e il latte '(S)he bought bread and milk' Yet other types of lists are possible (cf. Bonvino and Masini 2007 for a preliminary study, but also Gerdes and Kahane in prep.). A list which features the repetition (for two, three or more times) of the same lexical material in the same position conveys a general meaning of intensification that, we may suppose, specialises according to the categorial nature of the repeated constituent. For example, the repetition of the adjective piccola 'small' in (28) acts as a superlative, while the repetition of the verb in ( 29), as noted by Bertinetto (1991: 50), is a special way to express continuous aspect in Italian.

(28) Ho visto una casa piccola piccola 'I saw a little little house' A list which features the repetition of semantically related elements, especially co-hyponyms may convey a meaning of lexical approximation (30).

(30) C'era un elenco, un sommario, un indice insomma 'There was a list, a summary, an index let's say' We propose in Figure 1 a tentative representation of the relations observed between the listing phenomena mentioned above. Albeit preliminary, this representation shows that the use of a topological methodology allows to provide a unified account for a number of constructional phenomena usually treated under different domains. To sum up, topological patterns can be viewed as indefinitely extended, bi-dimensional, syntactic patterns, defined regardless of the boundary between the clausal and the supra-clausal level and (at least at the most abstract level) regardless of the categories they are made up of. These formal patterns are "meaningful" to a certain extent.

Topological patterns as constructions

The existence of "meaningful" abstract patterns naturally recalls the notion of "construction" in construction grammar. We would propose therefore to consider topological patterns as a type of constructions that operate at the level of discourse configurations.

Including topological patterns among the array of constructions is in line with some important recent attempts to break the boundary of the clause/sentence [START_REF] Mithun | The extension of dependency beyond[END_REF][START_REF] Mithun | The extension of dependency beyond[END_REF] and to extend the notion of construction to upper-level entities [START_REF] Fried | Construction Grammar: A Thumbnail Sketch[END_REF][START_REF] Fried | Construction Grammar and spoken language: The case of pragmatic particles[END_REF][START_REF] Östman | Construction Discourse: A Prolegomenon[END_REF]). In fact, as made clear by [START_REF] Fried | Construction Grammar and spoken language: The case of pragmatic particles[END_REF] and Östman (2005), construction grammar, as a theory, has no built-in limitation with respect to the extension of the notion of construction to larger stretches of discourse. Yet, only a very limited number of works on constructions deal with upper-level entities. Among them, Östman (2005) should be mentioned, who suggests that constructions can be detected at the textual level, claiming that there exist "discourse patterns" with a form (i.e. text type) and a meaning or function (i.e. genre).

Our paper follows this line of research. However, whereas Östman (2005) extends the notion of construction to entire texts and claims that this textual setting is essential for interpreting certain sentences correctly, in this paper we hypothesize that there exist constructions insensitive to the boundary of the clause/sentence and defined by their topological structure. Like all constructions, they can be more or less specified and enter inheritance systems.

The analysis of magari in what follows will be driven by these theoretical hypotheses. [START_REF] Pietrandrea | The grammatical nature of some epistemic-evidential adverbs in Spoken Italian[END_REF] has-albeit cursorily-observed that, although distributional regularities cannot be found at the clause level, magari has a regular topological distribution in discourse configurations. In particular, she noted that 42 out of the 75 tokens of magari occurring in a small corpus of the Roman variety of spoken Italian (about 56 percent), are associated with a specific kind of topological pattern: the focus of magari belongs to a list of items that realize the same syntactic position. In utterance (31), for example, the ARG 2 position is realized by four different arguments ('in a scene', 'in a forest', 'in a jungle', 'in the desert'), the first of which is in the focus of magari.

The analysis of magari

(31) Che ne so poteva comparire una scenografia che che magari li riportava ne in un ambiente, in una foresta piuttosto che in una giungla nel deserto [LIP] 'I don't know a set could appear that that maybe reconveyed them in in a scene, in a forest rather than in a jungle, in the desert' che ne so 'I don't know'

poteva comparire 'could appear' una scenografia 'a set' che 'that' che 'that' magari 'maybe' li riportava 'reconveyed them' ne 'in' in un ambiente 'in a scene' in una foresta 'in a forest' piuttosto che 'rather than' in una giunga 'in a jungle' nel deserto 'in the desert' ARG 1 ADJ 1 PRE ARG 2 ADJ 1 PRE ARG 1 ADJ 2
This strong tendency to occur in lists induced [START_REF] Pietrandrea | The grammatical nature of some epistemic-evidential adverbs in Spoken Italian[END_REF] to semantically characterize magari, commonly understood as an epistemic adverb, as a generic marker of non factuality, more precisely as a marker of "non exclusion of factuality" (NEF). In other words, putting forward the constituent in the focus of magari as but one of a set of possible options, the speaker does not fully subscribe to the factuality of the proposition realized through that constituent ('that reconveyed them in a scene'): (s)he simply does not exclude that that proposition could be factual.

We have further extended Pietrandrea's analysis with the aid of two large, diatopically balanced corpora of both spoken and written contemporary Italian, namely: the la Repubblica corpus (written, approx. 380 million tokens, cf. [START_REF] Baroni | Introducing the "La Repubblica" Corpus: A Large, Annotated, TEI(XML)-Compliant Corpus of Newspaper Italian[END_REF]) and the Lessico di Frequenza dell'Italiano Parlato (LIP) corpus (spoken, approx. 500.000 tokens, cf. De [START_REF] Mauro | Lessico di frequenza dell'italiano parlato[END_REF]).

We randomly selected 600 occurrences of magari (300 in the written corpus and 300 in the spoken corpus). For the sake of consistency, we subtracted from this first corpus 35 occurrences (32 spoken and 3 written) that could not be easily interpreted, such as for example (32), where the speaker interrupts himself right after uttering magari, thus making a proper classification impossible:

(32) Cioè non vorrei scartare questa possibilità a priori insomma magari 'I mean I wouldn't want to rule this out from the outset, I mean, magari'

We analyzed the remaining 565 occurrences of magari within the context of their discourse configurations; i.e., we took as a relevant unit of analysis the whole chunk made up of the sequence of units that instantiate or repeat the predicate-argument-adjunct structure that each occurrence of magari contributes to define.

A first thorough analysis of this corpus allowed us to identify the five main functions of magari mentioned in section 1. Afterwards, both authors coded separately the entire data set. The more problematic cases were discussed together.

This led to exclude, for the sake of simplicity, the 20 occurrences of magari (9 spoken and 11 written) that fulfilled more than one function. Thus, for example, we excluded occurrences such as (33), where magari functions at the same time as a concessive and as a scalar marker. 5 The final corpus therefore amounts to a total of 545 (286 written and 259 spoken) occurrences of magari.

(33) Ce la mettono tutta, magari scrivono anche bei pezzi, ma sono troppo limitati, possono esprimersi solo parzialmente [laR] 'They try hard, they might even write nice pieces, but they are too limited, they can only partially express themselves'

The discussion of the more problematic cases also led to a more precise semantic characterization of the five functions associated to magari, which can be defined as follows:

• equipotential non exclusion of factuality (ENEF);

• scalar non exclusion of factuality;

• scalar concessive conditional;

• weakened imperative;

• optative.

The quantitative results of our investigation on the final sample are given in Table 1. The data in Table 1 show a complex picture. First of all, the five functions of magari are not equally distributed across the corpus: the scalar and the ENEF functions cover together 79 percent of the occurrences of magari in the corpus (58 percent and 21 percent respectively), whereas concessives and imperatives are more marginal (10 percent and 9 percent respectively) and optatives are very infrequent (2 percent of the occurrences). Secondly, the association of magari with lists is regular: 349 occurrences of magari out of 545 (64 percent) have in their focus a constituent belonging to a list. It should be noted that, far from being a phenomenon typical of spoken language, the written occurrences of magari present an even more regular association with lists (69 percent). It can also be observed that, with the exception of optatives, which are by the way very rare, magari tends to be associated with lists no matter its exact function. See Graph 1. Without list

Yet the association of magari with lists is not equally distributed across the various functions (χ 2 = 71,48, df= 4, p<0, 001). As is shown in Graph 2, scalar and concessive magari clearly prefer the association with lists, whereas optative, imperative and (to a lesser extent) ENEF magari tend to be associated with lists less than expected. The five functions of magari are not even equally distributed across modalities: indeed, there is a significant interaction between the various functions of magari and the spoken vs. written modality (χ 2 =121,05, df=4, p <0,001). 6 In particular, scalar uses are more frequent in writing than expected, while all other uses are preferred in spoken data. These regularities are indicated in Graph 3. Another significant regularity emerges from the observation of the distribution of the five functions across modalities x [+list] vs.

[-list] constructions (χ 2 204,57, p <0,001). 7 As represented in Graph 4, in fact, it is clear that the ENEF magari retains its preference for spoken modality, regardless of its association with lists, whereas the strong preference of imperatives for spoken modality breaks down with list constructions. The concessive magari prefers list constructions regardless of modality, whereas the scalar magari prefers written modality regardless of its association with lists. Finally, optatives disprefer the association with list constructions regardless of modality. All in all, the analysis of the distribution of the five functions of magari underlines the peculiar behaviour of the optative function, which is much less frequent than the others and does not occur in lists regardless of modality.

It will be clearer in what follows that, as theoretically hypothesized within the Behavioral Profile approach [START_REF] Divjak | Ways of intending: Delineating and structuring near synonyms[END_REF][START_REF] Divjak | Ways of intending: Delineating and structuring near synonyms[END_REF]Gries 2006, Gries 2006), the behavioral regularities observed at the distributional level have a relevance at the cognitive and constructional levels as well.

Magari as a focus particle

The tendency of the elements focused by magari to occur in lists has led us to consider this word as a particular type of focus particle. As shown by [START_REF] Nølke | Le regard du locuteur 2: Pour une linguistique des traces énonciatives[END_REF][START_REF] Nølke | Le regard du locuteur 2: Pour une linguistique des traces énonciatives[END_REF] and [START_REF] König | The Meaning of Focus Particles: A Comparative Perspective[END_REF], focus particles, such as the English also, even, only or the French même are particles endowed with a remarkable syntactic mobility, which have scope on a constituent and focus on a part of it, thereby interacting with the focus structure of the sentence in which they occur (König 1991: 10). By focusing on a part of the scope, in fact, focus particles relate the value of the focused expression to a set of paradigmatic alternatives. For example, in (34) also has scope on the entire sentences and focuses on Piero, relating the value "Piero" to a set of paradigmatic alternatives. This entails the presupposition that someone else has left:

(34) Piero has also left This property, that derives from the very notion of focus [START_REF] Rooth | A Theory of Focus Interpretation[END_REF], has been highlighted by [START_REF] Nølke | Le regard du locuteur 2: Pour une linguistique des traces énonciatives[END_REF][START_REF] Nølke | Le regard du locuteur 2: Pour une linguistique des traces énonciatives[END_REF], who defines the focus particles of French adverbes paradigmatisants ('paradigmatizing adverbs'), i.e. adverbs presupposing the existence of a paradigm of variables that act as alternatives to the element in their focus.

Magari presents all the features that are typical of focus particles: it is characterized by a noticeable syntactic mobility, it has scope on constituents of various type and size and it focuses on a part of them, relating this focused part to a set of alternatives. In (31), for example, magari has scope on the constituent li riportava in un ambiente 'reconveyed them in a scene' and focuses on ambiente 'scene', which is therefore related with a set of alternatives ('in a forest', 'in the jungle', 'in the desert'). The peculiarity of magari is that, in the vast majority of its occurrences, the set of alternatives is not merely presupposed, but concretely realized by the list of units occupying the same position of the focused element. As we will see, the characterization of magari as a paradigmatizing adverb will have important consequences for our analysis.

4.2.

Defining the topological structure associated with magari

Considering magari as a focus particle anchored to both a focus and a scope enables us to provide a more rigorous definition of the relevant portion of topological space associated with this word. This can be defined as the space on the grid delimited on the horizontal axis by the position of magari plus the extension of its scope and on the vertical axis by the extension of the list of elements occupying the same position of the focus of magari.

While the focus of magari is easily identifiable through classical tests, the extension of its scope is a less apparent matter. Following the rules established by Nølke (2001: 274) for detecting the extension of the scope of French focus particles, we will distinguish two cases. If magari is pronounced with a neutral intonation, as in (35), it scopes over the whole sequence of units to its right, until the intonational phrase ends. If magari is pronounced with a parenthetical intonation, as in (36), not only the sequence of units to its right, but also the immediately preceding phrase is included in its scope:

(35) magari TORNA SUBITO, se non è proprio scemo 'He might come back immediately, if he's not completely stupid' (36) STARÀ CANTANDO, magari SOTTO LA DOCCIA, LA SUA CANZONE PREFERITA 'He might be singing, maybe in the shower, his favourite song' How are sentences with broken scope like (36) to be represent in grids? The rules mentioned in section 3.3 impose a representation of the sentence in (36) as in (37). In order to account for the fact that in the abstract predicate-argument-adjunct structure magari has scope over the entire clause, we should write it in the down left position; however, in order to preserve the linear order of the sequence, we should also write it one line below with respect to the first constituent uttered.

(37) Grid representation of (36) The topological structure relevant for our analysis is now univocally defined. Henceforth, it will be visually delimited by a thicker border, as shown in ( 38) and (39). It should be noted that this is a mere topological unit, which can be instantiated by items of very different type and size ranging from the sole magari, as in (38), to an entire text, as in (39).

(38) Magari! 'I wish (it were like this)!' This structure can be defined in constructional terms as a semispecified topological structure characterized not only by the presence of a fully lexically specified item (magari), but also, in most cases, by a specific topological pattern. The latter can be described as a list of equivalent items that occupy the very same position as the focus of magari and that can be of different type and size.

Although this abstract structure recurs, no matter what the exact function of magari is, the exact form of the list changes according to the function of magari. In the following sections, this phenomenon will be examined in detail.

Equipotential non exclusion of factuality (ENEF)

About 21 percent of the occurrences of magari fulfill the function of presenting the focus of magari as an element whose factuality is not excluded on a par with the factuality of other elements. We call this function "equipotential non exclusion of factuality" (ENEF).

The speaker puts the element in the focus of magari and its alternatives on the same level. In doing so, (s)he does not exclude, but (s)he neither subscribes to the focused element, which is considered equally possible with respect to the other options.

Examples of ENEF magari are provided in ( 40) through ( 42 When used in this function, the focus of magari regularly occurs (60 percent of the occurrences in the two corpora, 77 percent in the written corpus) at the top of a list of elements that either occupy one and the same position, as in ( 40) and ( 41), or instantiate the same syntactic structure, as in (42).

Although in all the examples above magari fulfills the same semantic function, it should be noted that the constituent in its focus may belong to very different categories: it can be a prepositional argument (31), a nominal argument (40), an adjunct (41) or also a clause (42). This fact supports the hypothesis that it is the topological structure of the construction (in particular the position of the focus of magari at the top of a list), rather than other categorial variables, that is relevant for licensing the non factual reading of magari.

It is worth mentioning that the conjuncts that are listed below the constituent focused by magari can be introduced by disjunctive conjunctions-such as piuttosto che 'rather than' in (31) or o 'or', as in ( 40) through ( 42)-or by a second occurrence of magari, as in ( 43), which can function as a disjunctive connective according to Mauri (2008aMauri ( , 2008b)). Sometimes, especially when the list is long enough, the items can be listed without explicit conjunction markers. In all cases the list is interpreted as a disjunctive list.

(43) magari è lì da un attimo magari è lì da sempre 'maybe he's been there for a second, maybe he's been there forever' [from Alessandro Baricco, Oceano Mare, Milan, BUR, 1999] The regular association of magari with disjunctive lists suggests that the overall effect of equipotential non exclusion of factuality is constructional in nature. As already argued, magari is a general marker of non factuality. This marker happens to be regularly associated with lists. It is precisely this regular association with lists that turns magari into a more specific kind of marker, i.e., a marker of non exclusion of factuality. The fact that the list we are dealing with is disjunctive in nature adds still another feature. Indeed, the disjunctive list can be characterized as "the semantic relation which obtains between two" (or more) items "that are equally possible […] and are potential substitutes for each other" (Mauri 2008a: 25). Therefore, the fact that the focus of magari belongs to a disjunctive list suggests that it is put forward as an option not to be excluded on a par with the other listed options. This combination of features contributes to produce the interpretation of magari as a marker of "equipotential non exclusion of factuality".

4.4.

Scalar non exclusion of factuality

As much as 58 percent of the occurrences of magari in the corpus (78 percent in the written corpus) fulfill the function of scalar operator of non factuality, in that they trigger a scale of non factuality whose extreme position is occupied by the element in its focus. Examples are in ( 44) through ( 47 The scalar function can be considered a particular instance of the focusing character of magari. It was shown in section 4.1 that, as a focus particle, magari entails the existence of a certain number of propositions that form a paradigm. In (44), for example, the paradigm is comprised of the following propositions: 'they have been approved from on high three times', 'they have been approved from on high four times', 'they have been approved from on high five times'. In the function under examination, magari indicates that the constituent in its focus (the proposition 'they have been approved from on high five times') realizes the most extreme proposition in the paradigm, i.e. the most non factual one or, rather, the last one for which the speaker would not exclude the factuality. This imposes a directionality-and consequently a scalarity-to the paradigm, which turns into a scalar domain of non factuality, in which the proposition realized by the constituent in the focus of magari has the highest degree of non factuality.

As examples (44) through (47) make clear, when fulfilling this function, the focus of magari regularly (66 percent) occurs at the bottom of a list of constituents occupying the same syntactic position or realizing the same syntactic structure. Also in this case, it is clear that the constituents in the list may differ largely from each other in size and category: they can be nominal arguments (45), predicates (46), adjuncts (44) or even entire clauses (47). This suggests that the scalar meaning of magari is licensed by the peculiar topological structure associated with it, i.e., by the occurrence of the focus of magari at the bottom of a list of constituents.

Our analysis so far shows that the function of magari as a scalar operator of non exclusion of factuality is constructional in nature. The general non factual meaning of magari combined with a list yields an overall meaning of non exclusion of factuality, as shown in section 4.3. The fact that magari focuses on the last conjunct of a list-as already noted by [START_REF] Fauconnier | Étude de certains aspects logiques et grammaticaux de la quantification et de l'anaphore en français et en anglais[END_REF] and [START_REF] Kay | [END_REF] in their analyses of the French word même and the English word even-introduces in the same construction an entire domain (corresponding to the items listed above the one in the focus of magari plus the item in the focus of magari) and, at the same time, the most extreme item of that domain (corresponding to the focus of magari). Representing one of the listed items as the most extreme in the domain induces a ranking. Given the semantic nature of magari, the listed items are ordered for increasing degree of non factuality, more precisely they are ordered from the most likely to the last one for which the speaker would not exclude the factuality.

In spite of the well established association of scalar magari with list constructions, 42 percent of the occurrences of magari with this function are not associated with a list. We will account for these exceptions in section 4.8.

4.5.

Scalar concessive conditional

About 10 percent of the occurrences of magari have a particular type of scalar function: they are scalar concessive conditionals. An example was provided in (3), another one is in ( 48):

(48) Ciascuna di queste vicende è, magari, piccola; ma la loro somma è un grande dramma [laR] 'Each of these events is, maybe, small; but their sum is a great tragedy'

The name "scalar concessive conditional" has been proposed by [START_REF] Haspelmath | Concessive Conditionals in the Languages of Europe[END_REF] to indicate concessive constructions such as that in ( 49):

(49) Even if we do not get any financial support, we will go ahead with our project

This construction can be regarded as a particular conditional construction in which "a set of protases is related to an apodosis" (Haspelmath and König 1998: 565). In (49) the set of protases is made up of the various conditions evoked by the scalar operator even (if we get great financial support, if we get some financial support, if we do not get any financial support). These conditions are clearly ranked in a scalar domain according to degree of adversity for the situation described in the apodosis, the condition in the focus of even (if we do not get any financial support) being considered as the most adverse. In scalar concessive conditionals, the set of protases describes non factual conditions, whereas the apodosis is normally factual. 8 It is exactly the combined effect of the factuality of the apodosis and the adversity of the circumstances described in the adverbial clause that triggers the concessive interpretation of this conditional construction.

Examples such as (48) can be considered as particular cases of scalar concessive conditionals. Magari in fact evokes a set of conditions arranged in a scalar domain: 'whether each of these events is remarkable', 'whether each of these events is normal', or 'whether each of these events is small'. These conditions are non factual-due to the presence of magari-and they are ranked not only according to degree of adversity but also to degree of non factuality. The condition in the focus of magari (ciascuna di queste vicende è piccola 'whether each of these events is small') is therefore not only the most unfavorable, but also the most unlikely. The main clause, however, is clearly factual.

As shown in the grid representations in ( 50) and ( 51), when magari fulfills the function of scalar concessive conditional, its focus is always a non factual item that occupies the first position of a list made up of at least two conjuncts, the last of which is introduced by an adversative conjunction (ma/però 'but', invece 'whereas'):

(50) Il comandante Arguelles si aspettava quindi un temporale, magari violento ma facile da superare [laR] 'Captain Arguelles therefore expected a possibly violent, but easy to overcome storm' Also in this case, the conjuncts in the focus of magari may be constituents of different category and size, such as adjuncts (50) or clauses (51). Therefore, it is only the kind of topological structure associated with this use of magari that licenses its scalar concessive meaning. On the one hand, the list within the topological structure of magari instantiates a particular type of list: [X 1 (X 2 , …), ADVERSATIVE CONJUNCTION, X LAST , where X 1 (X 2 , …) = <non factual>, X LAST = <factual>]. This abstract scheme is also typically associated with non factual concessive meanings in Italian:

(52) Può essere che è intelligente, però non lo dimostra 'It is possible that (s)he is clever, but (s)he doesn't show it'

On the other hand, the occurrence of magari in a conditional concessive context licences its scalar reading. Magari, as well as other focus particles (such as the Italian anche/pure 'also' or the German auch 'also'), always acquires a scalar meaning in conditional concessive contexts. As shown by König (1991: 64), this reinterpretation depends on the Gricean maxim of Relevance: "if a conditional connection between two eventualities is asserted and presupposed, it is invariably the more remarkable case that it is asserted". Thus in (50) it would be trivial to assert that the storm expected by the captain may be mild. This eventuality is presupposed, whereas the more remarkable case 'the storm may be violent' is asserted. This tendency entails that the focus of the conditional concessive magari is usually interpreted as the most extreme item in a scalar domain of conditions not to be excluded, i.e., the conditional concessive magari is always interpreted as scalar.

Imperative

About 9 percent of the occurrences of magari in the corpus have in their focus an imperative (53) or a related construction [START_REF] König | Speech Acts Distinctions in Grammar[END_REF], such as a hortative (54) or a deontically modalized sentence ( 55).

(53) Magari diglielo, faglielo comunque capire che ci tieni a lui! 'Maybe tell him, anyway make him understand that you care about him!' (54) Senti questo teniamolo, magari vediamolo alle prime bozze!

[LIP] 'Listen, let's keep this, maybe let's see it at the proofreading stage!' (55) Bisogna seguire un certo regime alimentare, bisogna magari mangiare un po' meno 'It is necessary to follow a certain diet, it is necessary, maybe, to eat a little less'

As shown by Elliott (2000: 76) and De Haan ( 2004), the presence of a marker of non factuality in imperative and related constructions is quite a common phenomenon across languages. This association may be motivated by the fact that commands describe non factual situations, which favors the presence of a non factual marker (see Elliott 2000: 76). Nevertheless, as mentioned in section 1, magari does not merely harmonically mark the non factuality of the command, but-as often happens crosslinguistically [START_REF] Mithun | The extension of dependency beyond[END_REF]-it also fulfills another function: it serves to weaken the force of the command (or exhortation). For example, the commands in (53) are considered as less mandatory, and consequently more polite, than their counterpart in (56) where magari is absent:

(56) Diglielo, faglielo comunque capire che ci tieni a lui! 'Tell him, anyway make him understand that you care about him!'

Needless to say, the weakened imperative function of magari is marginal in the written corpus, while it is attested in as much as 18 percent of the occurrences in the spoken corpus.

As the examples ( 53) to ( 55) and the grid representations below show, the imperatives in the focus of magari often occur in lists. This holds for about 32 percent of the imperative magari in our corpus. The imperatives may occur at the top of a disjunctive list, as in ( 57), or at the bottom, as in (58), in which case they also have a scalar meaning:

(57) Grid representation of ( 53 The occurrence of the imperative focused by magari in a list of imperatives makes it clear how magari weakens the illocutionary force of the imperative. When the speaker puts the focus of magari at the top of a list of alternatives (s)he invites the listener to take his/her command into account as but one of other options. When (s)he puts the focus of magari at the bottom of a list of commands he puts forward the focused command as to be executed as a last resort. It is clear that the weakened imperative function of magari, is, as well as the other functions, constructional in nature. The imperative (or its related constructions) endows the construction with the illocutionary force of a command. The non exclusion value of magari, combined with the occurrence of its focus in a list, is used to present the focused command as an option which is not to be excluded.

Optative

Less than 2 percent of the occurrences of magari in the corpus have an optative function such as that represented in the following example:

(59) Magari fosse così semplice! 'I wish it were so simple!'

It has been shown by Pietrandrea (2008b) that, when introduced in Italian in the 13 th century, the word magari-etymologically related to the Greek makarios ('blissful')-only had an optative meaning. It was usually employed as a predicative adjective uttered with an exclamative intonation referring to a sentential subject introduced by the complementizer ke 'that', as in (60):

(60) Makare ke -mme abberanno uccisa! 'If only they killed me!' [Iacopone da Todi, XIII laude del Laudario Urbinate, 13 th century]

When fulfilling the optative function, magari is always associated with an exclamative intonational profile. As the examples below show, in the scope of magari there can be a past subjunctive (61), an infinitive (62), a non verbal element (63) or even a Ø element as in (6), reproduced in (64):

(61) Magari venisse! 'I wish he would come!' (62) Magari averne! 'I wish I had!' (63) Magari due! 'I wish (there would be) two of them' (64) A: Vuoi un po' di riposo?

'Do you want to rest a bit?' B: Magari! 'I'd love to!'

Apparently the focus of the optative magari is never associated with topological structures characterized by lists. Pietrandrea (2008b) suggests that a relation of semantic bleaching exists between the optative and the non exclusion of factuality function of magari. Such a bleaching may have been historically induced by ambiguous contexts and reinforced precisely by the coalescence of magari within constructions characterized by lists. In fact, as pointed out by Pietrandrea (2008c), an optative meaning can be conceived of as the indication of a selection among a set of alternative (SoAs). Consequently, the occurrence of magari within list constructions (where more than one alternative option is expressed) has the effect of weakening the meaning of selection and favouring a more general non factual reading.

Synchronically speaking, the optative and the non exclusion of factuality uses of magari are nevertheless related to one another in that they both express non factuality.

Exceptions

The fact that the focus of the optative magari never belongs to a list has been theoretically explained in the previous section. However, we know from the data in Table 1 that the foci of ENEF, scalar and imperative magari are also not necessarily part of a list. This phenomenon characterizes 36 percent of the occurrences in the corpus and, therefore, it represents an exception to be explained.

Let us consider the cases in which magari fulfills an ENEF function, but its focus does not belong to a list, as in the following example:

(65) Non rischiò, non operò scelte che magari potevano suscitare contrasti [laR] '(s)he didn't risk, (s)he didn't make choices that maybe could cause disagreements' We may hypothesize that magari behaves in this context as a regular focus particle. It merely presupposes, without realizing it, the existence of a paradigm of unspecified alternatives to the focus of magari. For example, the clause in the focus of magari in (65) (potevano suscitare contrasti 'could cause disagreements') evokes a paradigm of other unspecified, but semantically related, possible alternatives which are not explicitly mentioned in the text, such as: potevano provocare proteste 'could cause protests', potevano procurare inimicizie 'could cause hostility', etc. Therefore, it may be hypothesized that this type of magari has inherited the property of evoking paradigms of elements alternative to its focus precisely from its more frequent association with fully realized lists.

A similar line of reasoning might be applied to the occurrences of magari in imperatival contexts. Thus a sentence like (66) evokes, without realizing it, a paradigm of alternative commands ('tell him', 'don't tell him'), thereby weakening the illocutionary force of the imperative.

(66) Magari diglielo 'Maybe tell him/her' Another exception to be dealt with regards the scalar function of magari. About 34 percent of the scalar occurrences of magari appear in contexts without a list. These are cases like those represented in the following example: In this construction magari and its focus have a parenthetical intonation. This characteristic leads us to put forward a possible explanation for these apparently exceptional cases. Indeed, according to the rules established in section 3.3 for grid representations, when the constituent immediately preceding magari is parenthetical, it should be included in its scope. As a consequence, the grid representations of (67) would be akin to that provided in (68):

(68) Grid representation of ( 67 If we rely on this representation, we can hypothesize that magari has focus on a constituent that lies at the bottom of a "partially instantiated" list.

The constituent in the focus of magari is an adjunct that modifies the backgrounded part of the scope. In (67), for example, magari focuses on the adjunct toscani 'Tuscan', which modifies the backgrounded item (di vini 'about wines'). This item is given the first time without modifications in the sequence dovrei parlarvi di vini 'I should talk to you about wines'. It is then modified, without an explicit repetition, in the sequence magari toscani 'possibly Tuscan'. The modification, without reiteration of the backgrounded part of the scope, means that it is elided. The overall effect is that a sequence such as ( 67) is interpreted as equivalent to the following: In (69), the modifying adjunct focused by magari-toscani 'Tuscan'-lies at the bottom of a list of two adjuncts. The first of these adjuncts (position ADJ 2 -line1) is a Ø element, i.e., the position is empty. Consequently, it conveys a meaning such as "non qualified (wines)" and the whole sequence is interpretable as: In conclusion, the presence of the modifying adjunct at the bottom of the partially instantiated list would trigger a scale of non factual propositions. The actualization of a more specific eventsuch as that described by the proposition 'I talk to you about Tuscan wines'-is in fact to be conceived as less likely than the actualization of a more general event-such as that described by the proposition 'I talk to you about wines'.

(69) […] dovrei parlarvi di vini,
To sum up, two hypotheses can be put forward in order to explain the cases in which the focus of magari does not belong to a list and to relate these cases to other more frequent cases with lists. The first hypothesis, which virtually applies to all exceptional cases, is that magari evokes a paradigm of possible alternatives with respect to the element in its focus by virtue of its frequent association with concretely realized lists. The second hypothesis only applies to scalar occurrences. In these cases the constituent in the focus of magari is always parenthetical and can be seen as the second conjunct of a partially instantiated list. In both cases, the presence of a list is posited.

This entails that from a cognitive, if not linguistic, point of view the focus of magari always belongs to a list, either fully instantiated, or partially instantiated, or simply evoked. This association of magari with a list would mark its general non exclusion of factuality meaning.

The network of magari constructions

As mentioned in the introductory sections of this paper, the main goal of our investigation is to understand which contexts license the various functions of magari and whether there is a relation between these functions (and of course which sort of relation). In order to reach this goal, we set our analysis within the general theoretical framework of construction grammar, which in principle allows to treat contexts as linguistic objects, and then we used a specific working methodology, namely the topological methodology, which allowed us to identify a set of topological structures in which magari regularly occurs. In this section we will give a more refined constructionist account of our findings.

The analysis carried out in section 4 shows that we can distinguish two main magari constructions:

• the optative magari construction;

• the map of non exclusion of factuality (NEF) magari constructions:

-ENEF; scalar NEF (with fully and partially instantiated list); scalar concessive conditional; weakened imperative.

As we briefly discussed in section 4.7, the optative magari presents specific distributional properties that distinguish it from other magari constructions: it is very infrequent, it does not occur with lists and it is always associated with an exclamative intonational profile. However, the two constructions are not completely independent from one another. Firstly, Pietrandrea (2008b) showed that there exists a diachronic semantic bleaching from optative to non exclusion of factuality, thus positing a sort of "diachronic link" between the two constructions. Secondly, from the point of view of our synchronic analysis, the two constructions share the presence of magari and a general "non factuality" feature.

As for the set of NEF magari constructions, we identified a class of topological structures in which magari occurs regularly. All these structures refer to a more general topological structure that can be represented as in Figure 2: the lexically specified adverb magari is followed by its scope, which is made up of a background and a focus; the latter is part of a list, i.e. is one of the listed elements. It is important to note that there is no explicit information about levels, categories, word order or sentence types, so all this information is underspecified, as well as the type of list involved. All the different magari constructions analysed in the sections above are more specified instances of the maximally abstract construction outlined in Figure 2. In other words, these constructions have some properties that specify the abstract construction (partially) described in Figure 2. These properties are listed below:

• ENEF magari construction:

-LIST = disjunctive -FOCUS = X 1 • scalar NEF magari construction (fully instantiated list):

-FOCUS = X LAST • scalar concessive conditional magari construction:

-X 1 (X 2 , …) = <non factual> vs. X LAST =< factual> -FOCUS = X 1 • imperative magari construction:

-SENTENCE TYPE = imperative -SPEECH ACT = command, exhortation, etc.

If we accept the hypothesis of the partially instantiated list put forward for the exceptional cases of magari with a scalar function (cf. section 4.8), then we still have another construction with the following overriding properties:

• scalar NEF magari construction (partially instantiated list):

-LIST = [x 1 , x 2=last ], in which x 1 =Ø -FOCUS = x 2=last -INTONATION: parenthetical
Therefore, from a constructionist perspective, the distribution of the non exclusion of factuality magari can be accounted for by

magari + SCOPE = [ BACKGROUND + FOCUS ] LIST = [X 1 , X 2 , …, X LAST ]
positing a hierarchy of closely related topological structures, each of which is regularly associated with one determined function of magari and all of which are linked to a more abstract construction with the general meaning of <non exclusion of factuality> and the topological structure described in Figure 2. The network of magari constructions emerging from our results is presented in Figure 3. Before commenting on this figure, it is worth discussing some of the conventions used. First, we made use of the inheritance links proposed by [START_REF] Goldberg | Constructions. A Construction Grammar Approach to Argument Structures[END_REF] (cf. section 3.1) to relate the various constructions at issue. Second, regarding the representation of the constructions themselves, we adapted the boxes-within-boxes notation [START_REF] Fried | Constructing Grammatical Meaning. Isomorphism and Polysemy in Czech Reflexivization[END_REF][START_REF] Fried | Construction Grammar: A Thumbnail Sketch[END_REF] to our needs by incorporating the outline of the topological structure associated with magari as the "formal" part of the construction. Third, some elements are graphically highlighted in order to facilitate the reading of the network: the various magari constructions endowed with a topological structure are enclosed in boxes with thicker borders, whereas the overriding properties of each sub-construction are put in boldface. Constructions with an uncertain status are marked by a question mark near the inheritance link and enclosed in a box framed by a dotted line. Finally, as can be seen, Figure 3 does not contain the imperative magari. The representation of this construction is given in Figure 4 below, which we will comment on later. Now let us return to Figure 3.

Overall, the network of constructions proposed in Figure 3 reveals that the network of magari constructions is basically governed by Instance inheritance links (I I ). A maximally abstract Non factual magari construction instantiates both the Optative magari construction and the Abstract NEF magari construction. The other magari subconstructions are inherited from the Abstract NEF magari construction by means of instance inheritance links.

The Abstract NEF magari construction as represented in Figure 2 is also linked-by means of a Subpart inheritance link (I S )-to an independent List construction with the maximally abstract meaning of <relation between the listed items>, whose existence has been proposed in section 3.2. As already pointed out, it is precisely the presence of a list that somehow turns the general non factual meaning of magari into a <non exclusion of factuality> meaning. At the same time, the ENEF magari construction is linked-by means of an I S -to the Disjunctive list construction, which is an instance of the general List construction. 10 The main property of the Abstract NEF magari construction is that it features a topological list that includes the element which is in the focus of magari. At this level, however, the interaction between the list and the focus is still underspecified, as well as the list itself.

This information becomes more specified as we reach the lower levels of the hierarchy. Both the ENEF magari construction and the Scalar NEF magari construction (with fully specified list) specify which element of the list is in the focus of magari. In the former, the focus is at the top of the list, and the list is disjunctive; in the latter, the focus is at the bottom of the list.

According to the hypothesis put forward in section 4.8, the Scalar NEF magari construction might instantiate another construction-the Scalar NEF magari construction with a partially instantiated list-whose topological structure is even more constrained. The list cannot contain more than two elements and the first one is a null element.

Finally, the Abstract NEF magari construction instantiates the Scalar concessive conditional construction, which includes a contrastive list in which one or more non factual elements are contrasted with a factual element. The Scalar concessive conditional construction is an instantiation of both the Abstract NEF magari construction and the (abstract) concessive construction, therefore we are dealing with a case of multiple inheritance. In addition, this construction is linked by a purely semantic link (represented here by a dotted line) to the Scalar NEF magari construction, since they share the scalarity feature.

As mentioned above, the Imperative magari construction is not present in this network. In fact, this is due to the fact that we interpret the Imperative magari construction as a further instantiation of both the ENEF magari construction and the Scalar NEF magari construction. As mentioned in section 4.6, and as reproduced in Figure 4, the Imperative magari construction may have the topological structure of both the former and the latter. In both cases, the corresponding meaning of magari is maintained and a general function of weakening of the command/exhortation is added. Therefore, the Imperative magari construction can be seen as a lower-level construction in which sentence type and speech act information is specified. Also, the two constructions are linked to one another (by a dotted link), since they share the Sentence type and Speech act features. In conclusion, the proposed constructionist analysis allows to connect all magari constructions with one another in an inheritance hierarchy and therefore gives us a better understanding of the speaker's knowledge of this piece of grammar.

Conclusions

The word magari has a number of grammatical meanings: equipotential non exclusion of factuality, scalarity, concessivity, weakening of the illocutionary force of the imperative and optativity. All these meanings proved to be constructional in nature, i.e., they are determined by the various constructions in which magari occurs. These constructions were efficiently identified by looking at topological patterns, i.e. structures that are recognizable at the discourse configuration level. This level of analysis, defined by the maintenance of a given predicateargument-adjunct structure in discourse, crosses the traditional divide between clausal and supra-clausal level and can only be characterized in terms of its topological structure.

The distribution of magari within discourse configurations has revealed interesting regularities. With the exception of the more marginal and more ancient optative function, magari is regularly associated with certain abstract topological patterns that can be characterized as lists containing the element focused by magari. The exact shape of this topological pattern is the only distinctive property that allows to univocally identify each type of magari.

Finally, these meaningful topological structures can be reinterpreted as proper "constructions", whose peculiarity consists in that they are insensitive to the boundary between clauses and are bi-dimensional in nature. They can also be represented in an inheritance hierarchy, which shows how the different magari constructions are inherited from a maximally abstract construction. fmasini@uniroma3.it, pietrand@uniroma3.it. The research was carried out within the Topogram project (Università Roma Tre) on the topology of grammatical meaning in discourse constructions. We would like to express our graditude to Claire Blanche-Benveniste, Elisabetta Bonvino, Claudio Iacobini, Sylvain Kahane, Alessandro Lenci, Henning Nølke and Raffaele Simone, who read previous drafts of this paper and provided invaluably helpful comments and suggestions. A special thank goes to Ewa Dąbrowska, Editor-in-Chief at Cognitive Linguistics, who guided us through a very fair and stimulating revision process, and to an anonymous Associate Editor and two anonymous referees, who sensibly improved our paper with their comments. The usual disclaimers apply. 1. Polysemy links (I P ) "capture the nature of the semantic relations between a particular sense of a construction and any extensions from this sense" (Goldberg 1995: 75); subpart links (I S ) are posited when "one construction is a proper subpart of another construction and exists independently" (1995: 78); instance links (I I ) are posited when a construction "is a more fully specified version" of the construction it is linked to (1995: 79); finally, metaphorical extension links (I M ) are posited when "two constructions are found to be related by a metaphorical mapping" (1995: 81). 2. The analysis presented in this article was carried out with the aid of real examples. In particular, we made use of corpora of contemporary written and spoken Italian, respectively la Repubblica corpus [laR] and Lessico di frequenza dell'italiano parlato [LIP] (see section 4 for further information about these corpora); in addition, we took examples from the Web [Web] and contemporary novels. Examples taken from the mentioned corpora or the Web are marked with the corresponding abbreviation in squared brackets at the end of the example. Texts taken from novels include the full reference of the novel. Intuition-based examples, on the contrary, have no indication. 3. Apart from the ARG, ADJ and PRE abbreviations for 'argument', 'adjunct' and 'predicate', respectively, we sometimes use other labels, namely: ASP (aspectual element), CAUSE (causative element) and MOD (modal element). Besides, note that the translations of the examples throughout the paper are deliberately as literal as possible in order to facilitate the grid representation.

4. For example, the discourse configuration in ( 21) is characterized by two lists of arguments in the ARG 1 and ARG 2 positions; one repetition of syntactic structure (line 1 and line 2) and a chiasm between the first two realizations of the ARG 1 and ARG 2 positions. The pre-verbal hyperonym in ARG 1 -line1 position per ogni tipo di gioco 'for every kind of game' is exemplified by a post-verbal hyponym in ARG 2 -line2 alle corse dei carri 'for the chariot races', whereas the post-verbal hyperonym in ARG 2 -line1 position un edificio specifico 'a specific building' is exemplified by a pre-verbal hyponym in ARG 1 -line2 il circo 'the circus' (Bonvino 2005: 61). 5. These are cases of unifications, which are extremely interesting from a theoretical point of view. However, for our current purposes, they would have biased the overall picture. 6. We thank the Associate Editor who reviewed the paper for pointing this out. 7. See note 6. 8. König and Haspelmath (1998: 573) discuss some marginal exceptions to the factuality of the apodosis, but they are not relevant for our purposes. 9. Constructions like (69) are indeed grammatical and attested. See, for example, the following instances: (i) poi si vedrà, se troverò il tempo per dedicarmi ad un uomo, magari un uomo vero 'then we will see, if I will find the time to dedicate myself to a man, possibly a real man' (ii) "C'era una volta" sarebbe un inizio perfetto per cominciare una storia, magari una storia per bambini '"Once upon a time" would be a perfect beginning to start a story, possibly a story for children' 10. It should be noted that this link is not strictly necessary, since the Disjunctive list may instantiate directly within the ENEF magari construction, that inherits the more general List construction from the Abstract NEF magari construction. We however decided to maintain this link for the sake of explicitness, and more precisely to highlight the semantic contribution of the disjunctive list to the whole ENEF construction.

Figure 1 .

 1 Figure 1. The constructional network for "lists"

Graph 1 .

 1 The association of the five functions of magari with lists

Graph 2 .

 2 Interaction between the five functions of magari and their association with lists

Graph 3 .

 3 Interaction between the five functions of magari and their occurrence across modalities

Graph 4 .

 4 Interaction between the functions of magari and their occurrence across modalities and list constructions

(

  67) [...] dovrei parlarvi di vini, magari toscani [laR] '[…] I should talk to you about wines, possibly Tuscan (wines)'

(

  70) […] dovrei parlarvi di vini quali che siano, magari di vini toscani '[…] I should talk to you about whichever wines, possibly Tuscan wines'

Figure 2 .

 2 Figure 2. The topological structure of the Abstract NEF magari construction

Figure 3 .

 3 Figure 3. The network of magari constructions

Figure 4 .

 4 Figure 4. Imperative magari constructions

Table 1 .

 1 Functions of magari in the corpus

		ENEF Scalar Concessive Imperative Optative Total	%
	Written	30	223	27	3	3	286 100%
	With list	23	145	27	1	0	196	69%
	Without	7	78	0	2	3	90	31%
	list
	Spoken	87	91	28	47	6	259 100%
	With list	47	63	28	15	0	153	60%
	Without	40	28	0	32	6	106	40%
	list
	Total	117	314	55	50	9	545 100%
	With list	70	208	55	16	0	349	64%
	Without	47	106	0	34	9	196	36%
	list
	%	21%	58%	10%	9%	2% 100%

  )

	1 magari	diglielo
	'maybe'	'tell him'
	2	faglielo		comunque	capire	che ci tieni a lui
		'make him'	'anyway'		'understand'	'that you care about him'
		CAUSE	ADJ 1		PRE
	ADJ 1	PRE				ARG 1
	(58) prova a calmarti un po' [...] e magari chiedi scusa alla
	mamma				[Web]
	'Try to calm down a bit and possibly apologize to your mother'
	1		prova		a calmarti	un po'
			'try'		'to calm down'	'a bit'
	2 e magari		chiedi scusa	alla mamma
	'and possibly'	'apologize'	'to your mother'
	ADJ 1		PRE		ARG 1	ADJ 2

  )

	1 dovrei	parlarvi		di vini
	'I should'	'talk to you'		'about wines'
	2		magari		toscani
			'possibly'		'Tuscan'
	MOD	PRE	ADJ 1	ARG 1	ADJ 2
	PRE		ARG 1

  Authors' affiliation: Dipartimento di Linguistica, Università Roma Tre, Via Ostiense 236, 00146 Roma (Italy). Authors' e-mail addresses:

	Received 7 April 2008	Dipartimento di Linguistica
	Revision received 27 October 2008	Università Roma Tre
		Roma, Italy
	Notes
	*


Emmanuel Vincent

Advances in audio source seperation and multisource audio content retrieval

Keywords: Speech, audio, source separation, robust automatic speech recognition

Audio source separation aims to extract the signals of individual sound sources from a given recording. In this paper, we review three recent advances which improve the robustness of source separation in real-world challenging scenarios and enable its use for multisource content retrieval tasks, such as automatic speech recognition (ASR) or acoustic event detection (AED) in noisy environments. We present a Flexible Audio Source Separation Toolkit (FASST) and discuss its advantages compared to earlier approaches such as independent component analysis (ICA) and sparse component analysis (SCA). We explain how cues as diverse as harmonicity, spectral envelope, temporal fine structure or spatial location can be jointly exploited by this toolkit. We subsequently present the uncertainty decoding (UD) framework for the integration of audio source separation and audio content retrieval. We show how the uncertainty about the separated source signals can be accurately estimated and propagated to the features. Finally, we explain how this uncertainty can be efficiently exploited by a classifier, both at the training and the decoding stage. We illustrate the resulting performance improvements in terms of speech separation quality and speaker recognition accuracy.

INTRODUCTION

In many environments, the audio modality consists of several sound sources. The target sound sources, which may be either specific speakers or sound events, are then masked by a variety of other sounds which make it difficult to understand speech or detect these events both for humans and computers. These issues can be broken down into two fundamental problems:

• source separation, that is estimating the audio signal of each source from the observed mixture,

• classification of the separated sources, e.g. automatic speech recognition (ASR) or acoustic event detection (AED).

In this paper, we review recent advances pertaining to these two problems in Sections 2 and 3, respectively. We conclude in Section by summarizing achievements and future perspectives 4.

SOURCE SEPARATION 2.1 State of the art

Audio source separation algorithms typically operate in the time-frequency domain by means of the short-time Fourier transform (STFT). The established linear modeling paradigm [START_REF] Makino | Blind speech separation[END_REF][START_REF] Vincent | Probabilistic modeling paradigms for audio source separation[END_REF] assumes that the sources are static point sources and that the amount of reverberation is low. Under these assumptions, the vector X nf of complex-valued STFT coefficients of the multichannel mixture signal in time frame n and frequency bin f is given by

X nf = J j=1 S jnf A jf (1)
Further author information: E-mail: emmanuel.vincent@inria.fr, Telephone: +33 (0)2 99 84 22 69

where S jnf are the scalar STFT coefficients of the J underlying single-channel source signals indexed by j and A jf are steering vectors representing the frequency response of the mixing filters. The source STFT coefficients are then typically assumed to be independent and identically distributed according to a sparse distribution and estimated in the maximum a posteriori (MAP) sense using convex or nonconvex optimization. Depending on the respective number of mixture channels and sources and on the chosen source distribution, this approach yields different algorithms called frequency-domain independent component analysis (FDICA) or sparse component analysis (SCA).

The series of Signal Separation Evaluation Campaigns (SiSEC) 3 * has shown that these algorithms achieve good results on mixtures of two sources with low reverberation but that their performance significantly degrades in the presence of many sources, background noise or medium to high reverberation. Indeed, they mostly rely on spatial cues, which are obscured in complex environments.

A general flexible probabilistic framework

In order to achieve more robust separation in such complex environments, a new variance modeling paradigm has emerged which enables the handling of diffuse or reverberated sources and the exploitation of spectral cues. [START_REF] Vincent | Probabilistic modeling paradigms for audio source separation[END_REF] The mixture STFT coefficients are now modeled as

X nf = J j=1 C jnf (2)
where C jnf is the spatial image of source j, that is its contribution within the mixture. This multichannel quantity is subsequently modeled via the zero-mean Gaussian distribution

C jnf ∼ N (C jnf |0, V ex jnf V ft jnf R jf ) (3)
where V ex jnf and V ft jnf represent respectively the spectral power of the excitation and that of the filter within a source-filter model of the source and R jf is the spatial covariance matrix of the source.

In the case of point sources with low reverberation, the spatial covariance matrices are rank-1 matrices which can be expressed as R jf = A jf A H jf where A jf are the steering vectors defined above. The main benefit of this new model comes when considering diffuse or reverberated sources: we have argued that R jf then become full-rank matrices which do not only encode the spatial position of the sources but also their spatial width. [START_REF] Duong | Under-determined reverberant audio source separation using a full-rank spatial covariance model[END_REF] We have also proposed to factor the spectral power of the excitation as 5

V ex jnf = klm W ex jf l U ex jlk G ex jkm H ex jmn ( 4
)
where W ex jf l , U ex jlk , G ex jkm and H ex jmn represent the spectral fine structure, the spectral envelope, the temporal envelope and the temporal fine structure of the source, respectively. A similar factorization may be assumed for the spectral power of the filter. Each of these quantities may be either fixed depending on the available prior knowledge about the sources at hand, or estimated from the data in an unsupervised fashion. For instance, in Figure 1, a speech source is modeled by assuming that its spectral fine structure is either harmonic or wideband and that its temporal fine structure exhibits a smooth temporal decay and by estimating its spectral envelope and its temporal envelope from the data. The estimated temporal envelope G ex jkm exhibits peaks for certain rows k encoding the pitch of the voiced part and the shape of the unvoiced part over time m. This flexible factorization makes it possible to exploit many more cues for separation than FDICA or SCA, thereby improving robustness to difficult mixtures where spatial cues do not suffice.

The model parameters can be estimated in the maximum likelihood (ML) sense via the expectation-maximization (EM) algorithm and the source STFT coefficients C jnf are then recovered by multichannel Wiener filtering. The source signals are finally obtained by STFT inversion. The resulting algorithm has been implemented in the Flexible Audio Source Separation Toolkit (FASST) † for Matlab. Table 1 shows the average signal-to-distortion ratio (SDR) in decibels (dB) achieved by FASST on two-channel reverberant mixtures of three and four speech sources from the SiSEC 2010 evaluation campaign, depending on the rank of the spatial covariance matrices and on whether the spectral and the temporal fine structures are constrained or not. The best results are achieved when both the spectral and the temporal fine structures are constrained as in Figure 1. Also, full-rank spatial covariance matrices greatly improve performance compared to rank-1 spatial covariance matrices when the microphone spacing is large.

Table 1. Average SDR achieved by FASST on two-channel reverberant mixtures of three and four speech sources from the SiSEC 2010 evaluation campaign, depending on the rank of the spatial covariance matrices and on whether the spectral and temporal fine structures are constrained (X) as in Figure 1 or not. Two different microphone spacings are considered.

CLASSIFICATION OF SEPARATED SOURCES

State of the art

While the source signals estimated by FDICA, SCA or FASST can be directly input to an ASR or an AED system, 6 this approach is suboptimal as shown in particular by the PASCAL CHiME Speech Separation and Recognition Challenge 7 ‡ . Indeed, the audio features such as mel frequency cepstral coefficients (MFCC) used by classification systems are typically not robust to the distortions of the sources produced by source separation systems. In order to overcome this issue, additional information must be passed along with the sources to the classification system describing which parts of the source signals have been estimated with high confidence and which have not.

The uncertainty decoding (UD) framework 8 addresses this issue in the case of Gaussian mixture model (GMM) or hidden Markov model (HMM)-based classification systems by assuming that the feature vectors are modeled by a Gaussian distribution whose mean and covariance matrix represent the expected value of the features and the uncertainty about this value, respectively. Assuming that a clean model has been learned for each class, this uncertainty information is integrated with the GMM/HMM likelihood so as to form a noise-robust likelihood In the case of Gaussian mixture model (GMM) or hidden Markov model (HMM)-based classification used for ML classification. In practice, the uncertainty over the features is obtained by uncertainty estimation over the source STFT coefficients followed by uncertainty propagation to the features via moment matching or unscented transform techniques. [START_REF] Astudillo | A MMSE estimator in mel-cepstral domain for robust large vocabulary automatic speech recognition using uncertainty propagation[END_REF] Despite advances in this area, uncertainty estimation techniques remain mostly heuristic to date. Also, the original UD framework exploits uncertainty information only at the classification stage but not at the training stage, so that clean data are needed for training the classifier.

Robust feature extraction

Let us denote by θ the set of parameters of the considered source separation system, e.g. the variables

R jf , W ex jf l , U ex jlk , G ex jkm , H ex jmn , W ft jf l , U ft jlk , G ft
jkm and H ft jmn in the case of FASST. One established uncertainty estimation technique consists of estimating θ = arg max P (X|θ) in the ML sense as explained in Section 2 and approximating the uncertainty P (C|X) over the source STFT coefficients by that of the multichannel Wiener filter P (C|X, θ) derived from θ.

We have argued that uncertainty is better estimated in theory by marginalizing over the parameters θ: P (C|X) ∝ P (X|C, θ)p(C|θ)dθ.

(

Due to the large number of parameters, this integral is typically intractable so we proposed a variational Bayesian (VB) inference algorithm yielding a tractable approximation. [START_REF] Adiloglu | A general variational Bayesian framework for robust feature extraction in multisource recordings[END_REF] Table 2 shows the average root mean square error (RMSE) between the true and the estimated source MFCCs for the two-channel reverberant speech mixtures and the various source models of Table 1, depending on the chosen uncertainty estimation technique. The proposed VB-based uncertainty estimation provides a small improvement compared to ML-based uncertainty estimation for all source models. The estimated covariance of the source MFCCs (not shown in the table) is also more accurately estimated.

Robust classifier training

The inability of UD to train classifiers from noisy data is even more crucial. Firstly, clean training data are not always available in the case of, e.g., field recording or mobile recording where the whole recording might be corrupted by noise. Secondly, even when sufficient clean data are available for training, the uncertainty over the test data is never perfectly estimated in practice such that some noise may remain that is not accounted for. Yet, training from noisy data is known to be an efficient technique to account for noise in the test data and improve the robustness of the classifier. ‡ http://spandh.dcs.shef.ac.uk/projects/chime/challenge.html Table 2. Average RMSE in dB between the true and the estimated source MFCCs for the two-channel reverberant mixtures and the various source models of Table We proposed an EM algorithm termed uncertainty training that estimates the parameters of a GMM-based classifier by maximizing the noise-robust likelihood of UD over the training data. [START_REF] Ozerov | GMM-based classification from noisy features[END_REF] Each iteration of this algorithm consists of estimating the first and second order moments of the feature vectors by Wiener filtering given the uncertainty about the training data and subsequently updating the GMM parameters.

Table 3 shows the results for a speaker classification task over mixtures of speech and real-world domestic background noise taken from the PASCAL CHiME Speech Separation and Recognition Challenge dataset. For both training and test data, separation is performed via FASST, uncertainty estimation via the ML-based approach cited above and MFCC uncertainty propagation via the vector Taylor series (VTS) technique. [START_REF] Ozerov | GMM-based classification from noisy features[END_REF] Speaker recognition accuracy is evaluated when training either from clean data, matched training data exhibiting the same signal-to-noise ratio (SNR) as the test data, unmatched data exhibiting a different SNR, or multi-condition data spanning all SNRs. Source separation combined with UD improves accuracy by 6 to 18% absolute compared to classification from the noisy signal. Uncertainty training further increases performance by 3 to 4% absolute when training from noisy data. The resulting performance is then much higher when training from multi-condition or even unmatched data than when training from clean data.

CONCLUSION

In the last five years, source separation has become a mainstream topic in audio signal processing. A few recent algorithms such as FASST have reached a sufficient level of maturity which enables their use in real-world reverberant, noisy application scenarios. The boom of mobile computing has also created a demand for robust ASR systems for handheld devices. Although commercial systems already exist, room remains for improving their robustness to challenging acoustic conditions. Recent advances in uncertainty decoding will most probably play a role in that context.

Figure 1 .

 1 Figure 1. Example factorization of the spectral power of a speech source.

  1, depending on the chosen uncertainty estimation technique.

	Spatial, spectral, and		Average
	temporal constraints	RMSE (dB)
	rank spec	temp	ML-based VB-based
	1			6.66	6.63
	2			6.85	6.84
	1	X		6.72	6.69
	2	X		6.82	6.80
	1		X	6.59	6.54
	2		X	6.76	6.76
	1	X	X	6.61	6.57
	2	X	X	7.23	6.92

Table 3 .

 3 Average speaker recognition accuracy (in %) for all training and decoding algorithms as a function of the training condition.

	Source	Training	Decoding		Training condition
	separation strategy	strategy	Clean Matched Unmatched Multi
	No	Conventional Conventional	65.17	71.81	69.34	84.09
	Yes	Conventional Conventional	55.22	82.11	80.91	90.12
	Yes	Conventional Uncertainty	83.48	87.92	87.19	90.12
	Yes	Uncertainty	Uncertainty	83.48	91.79	90.61	94.04

ACKNOWLEDGMENTS

This work was jointly performed with Kamil Adiloglu, Frédéric Bimbot, Ngoc Q. K. Duong, Rémi Gribonval, Alexey Ozerov and Laurent S. Simon and supported by Oseo under the Quaero program and the EUREKA Eurostars i3DMusic project.