Raheel Qader
email: raheel.qader@irisa.fr

Gwénolé Lecorvé
email: gwenole.lecorve@irisa.fr

Damien Lolive
email: damien.lolive@irisa.fr

Pascale Sébillot
email: pascale.sebillot@irisa.fr

Expression. * Équipe

Phonology Modelling For Expressive Speech Synthesis: a Review

Keywords: Phonology, pronunciation, disuencies, expressivity, speech synthesis, automatic

Expressive speech processing is an important scientic problem as expressivity introduces a lot of variability into speech. This variability leads to a degradation of speech application performances. Variations are reected in the linguistic, phonological and acoustic sides of speech.

However our main interest is on phonology, more precisely the study of pronunciation and of disuencies. Both of these elds have huge impacts on speech. This report is a bibliographical review of the state of the art in expressivity and phonology modelling. Although the main focus will be on speech synthesis, we will discuss works about automatic speech recognition as well because expressivity modelling in phonology is a cross-domain problem.

L'expressivité introduit beaucoup de variabilité dans la parole. Cette variabilité touche des aspects aussi linguistiques, phonologiques qu'acoustique et conduit généralement à des dégradation des applications de traitement de la parole. Ainsi, le traitement de la parole expressive est un problème important. Précisément, notre intérêt principal se porte sur l'étude la phonologie, plus précisément celle de la prononciation et des disuences, ces deux champs ayant chacun un rôle considérable dans la parole.

Ce rapport est une étude bibliographique des travaux liées à l'expressivité et à la modélisation de la phonologie. Le cadre de cette étude est principalement celui de la synthèse de la parole. Néanmois, comme la modélisation phonologique de l'expressivité est une problématique multi-domaine, nous aborderons également des travaux issus du monde de la reconnaissance automatique de la parole.

Mots clés :

Phonologie, prononciation, disuences, expressivité, synthèse de la parole, reconnaissance automatique de la parole.

Introduction

Human speech has two dierent distinctive aspects, the linguistic content which is conveyed from a speaker to another and the style in which the speech is uttered [START_REF] Eide | A corpus-based approach to expressive speech synthesis[END_REF]. Whereas the linguistic content is rather to bring direct information about the meaning, the impact of style is more implicit. In the recent years, in speech processing, style has been particularly studied through the spectrum of expressivity, that is the expression of dierent states of mind like emotions, so-called speaking styles (casual, formal, etc.) or intentions. Speech data exhibiting such characteristics is referred to as expressive speech, as opposed to neutral speech where style is absent.

Expressive speech processing is an important scientic problem as expressivity introduces a lot of variability into speech. In linguistics, expressivity may change the choice of words or of syntactic structures. In acoustics, it impacts various characteristics like the energy, pitch, duration, etc. In this PhD, we rather focus on the changes in phonology. Generally speaking, phonology is the study of sounds. In the context of this work, it will more precisely gather the study of pronunciation and of disuencies. Variabilities in pronunciation can appear through deletion, insertion or substitution of phones compared to standard pronunciation. For instance, the standard pronunciation of the word and is /aend/ in English, but in spontaneous speech it is mostly pronounced as /aen/, the nal phone /d/ being dropped. Regarding disuencies, expressive speech introduces phenomena like lled pauses, repetitions, etc. For instance, in unprepared speech, speakers tend to overuse lled pauses [START_REF] Corley | Hesitation disuencies in spontaneous speech: The meaning of um[END_REF], mainly because they are still planning the ow of their discourse while speaking.

These variabilities introduce many problems in speech applications and lead to a degradation in their performance. In this work, we are specically interested in Text-To-Speech (TTS) with some extensions to Automatic Speech Recognition (ASR). An overview of how TTS and ASR work Collection des Publications Internes de l'Irisa c IRISA provides probabilities of word sequences in the considered language. As a bridge between those two models, the pronunciation dictionary links each word to its phonetic representation. Among the various problems faced by these components, phonology-related problems mainly concern the pronunciation dictionary, and in a lesser extent the language model. Mainly the problem arises when the speaker pronounces words in an unusual way or words which are absent from the dictionary, the latter being called Out-Of-Vocabulary words (OOVs). Regarding disuencies, the problem is to consider their probability to appear in the middle of word sequences.

The purpose of this PhD is to study phonology modelling in the frame of expressive speech synthesis. The following is a list of the most important objectives that we will try to achieve during this PhD:

• Extracting and analysing characteristics of expressivity in speech corpora.

• Modelling phonology (pronunciation and disuencies) of expressive speech, with an emphasis on statistical/probabilistic approaches.

• Integrating expressive phonological models in a TTS system to generate expressive speech.

In addition, this PhD focuses on the symbolic representations of speech. Hence signal processing aspects will mainly be left aside. Instead, extensive usage of Natural Language Processing (NLP) techniques will be favoured. Finally, within the course of this PhD, major eorts will be spent on studying pronunciation modelling, while the problem of disuencies is considered as more exploratory.

Collection des Publications Internes de l'Irisa c IRISA This document seeks to review the state of the art in expressivity and phonology modelling.

Although the main focus is on speech synthesis, expressivity modelling in phonology is a crossdomain problem and this bibliographical study will thus discuss works spanning over both TTS and ASR. The remainder of this report is as follows. In Section 2, expressivity is dened and its types are explained. Sections 3 and 4 then review the literature about pronunciation and disuencies respectively. Finally in Section 5 a discussion about the work that we have done and the work that we are planning to do in the rest of the PhD is presented.

Expressivity

Expressivity is a complex concept. [START_REF] Govind | Expressive speech synthesis: a review[END_REF] denes it as the vocal indicator of various emotional states that is reected in the speech waveforms. More generally, emotional states can be extended to psychological characteristics of a speaker at a giving time, e.g., emotions, speaking style, personality, intention, etc. Expressivity makes human speech richer and more natural by adding an extra layer of non-linguistic information to the speech. A linguistic message can convey dierent meanings based on the expresivity factors that are added to it such as emotion, and speaking style. For instance, a linguistic message that is uttered with a high pitch and intonation at the end might be understood as a question, while the same utterance with a neutral pitch will be considered as normal phrase. According to [START_REF] Govind | Expressive speech synthesis using prosodic modication and dynamic time warping[END_REF], expressivity is considered to be the basic block of eective communication as it makes a conversation more eective and increase the involvement of listeners.

Emotion, speaking style and intention are all known to aect phonology, i.e. pronunciation and disuencies. In this PhD, we will be mostly concentrating on dierent speaking styles and accents as a specic case of speaking styles, without considering emotions. Nevertheless, emotions will be still discussed in the following section as it is an important part of expressivity. These aspects are dened and reviewed in this section.

Emotion

Emotions can be expressed in dierent forms. They can generally be labelled and categorized into positive and negative emotions. Positive emotions include joy, pride, love, relief, hope, compassion while negative ones include anger, anxiety, guilt, shame, sadness, envy, jealousy, and disgust [START_REF] Adda-Decker | Investigating syllabic structures and their variation in spontaneous french[END_REF]. In a ner way, emotions can be represented as points of a continuous space. Especially, [Russell, 1980] suggests a 2-dimensional representation of emotions where the rst dimension stands for pleasure-displeasure and the second for the arousal degree. Figure 2 places most known emotions in this space based on their characteristics. The horizontal axis is for pleasure while the vertical axis is for the arousal degree. For example, anger can be dened as a moderate displeasure (left side) and a neutral arousal (center of the axis). Using this representation, the closeness between emotions can be computed.

Studies have shown that speech and emotion have a very strong correlation and that emotion plays a critical role in communication [START_REF] Iida | A corpus-based speech synthesis system with emotion[END_REF]. Emotion might aect a speaker's choice of words i.e. the speaker mostly utters the type of words that reect his/her emotional state.

However, emotions are more tightly bound to acoustic characteristics rather than to linguistic ones.

The acoustic parameters that are linked to emotions consist of fundamental frequency, formant frequencies, intensity and duration [Schröder, 2009]. In TTS, availability of these parameters is necessary for the production and identication of emotion types. In ASR, the variability of these parameters based on a speaker's emotional state brings recognition rate drops compared to neutral speech [START_REF] Polzin | Pronunciation variations in emotional speech[END_REF]]. As the aim of this work is to study phonological variations of expressive speech using NLP techniques, emotions will be less studied in this PhD.

Collection des Publications Internes de l'Irisa c IRISA

Speaking style

The notion of "speaking style" is still ambiguous to most researchers, as speaking style not only varies from region to region but also from one person to another. According to [Parlikar, 2013],

the same speaker can adopt many dierent speaking styles based on the performed task. Speaking style is most likely to change based on the environment that the speaker is found in. For instance, a speaker usually has a relaxed speaking style when talking to a friend in an informal conversation, while the same speaker is likely to change his style of speech into a formal one during a corporate meeting. Dierent speaking styles can mostly be observed in spontaneous/casual speech, in which speakers prefer to communicate in their own style.

Several factors lead to the generation of dierent speaking styles among speakers. These factors include acoustic and phonological changes. Acoustic variations include intonation, duration, fundamental frequency, intensity and loudness [Laan, 1997] while phonological changes, as suggested by [START_REF] Adda-Decker | Pronunciation variants across system conguration, language and speaking style[END_REF], can be related to a variety of factors such as rate of speech, syllabic structure of words, individual speaker habits and regional dialect. These phonological changes occur at the phonemic level, for instance, insertion, deletion and substitution of phones. According to [Laver, 1994] (cited by [START_REF] Strik | Modeling pronunciation variation for ASR: a survey of the literature[END_REF]), changes occur as the degree of formality becomes less. In this study, we will look into to the phonological changes in depth.

Accents

Accent can be thought as a particular case of speaking style.

As such, it takes part in expressivity in general. Both native and foreign speakers of a language seem to have a specic accent. Native speakers are aected by regional accents while foreign speakers are aected by the patterns which they carry from their own language. As reported by [START_REF] Arslan | Language accent classication in american english[END_REF],

foreign speakers can be identied based on the appearance in their speech of certain patterns which cannot be found in the speech of native speakers. Foreign speakers who have acquired

Collection des Publications Internes de l'Irisa c IRISA

Grapheme to phoneme

Pronunciation dictionary

Post-lexical processing Text (words/graphemes) + Features Phonemes (+ syllables...) Phonemes (+ syllables...)

Target condition

Figure 3: Overview of the main modules and data involved in pronunciation modelling the language in an early age are also reported to be able to minimize their accent. Moreover, [START_REF] Arslan | Language accent classication in american english[END_REF] denes a foreign accent as the patterns of pronunciation features which characterize an individual's speech as belonging to a particular language group. In this research, we are rather interested in accents of foreign speakers in the rst place, as it is believed that patterns of foreign speakers are more obvious and easier to detect than those of native speakers.

In short, expressivity is an important characteristic of human speech that dierentiates speech of individuals from each other and makes speech more natural. However this usually leads to poor performances of speech applications. In the next section, some of the major concepts and studies within the area of expressivity and pronunciation modelling will be reviewed.

Pronunciation modelling and generation

In general, pronunciation modelling is a way to link the orthographic representation of written words with their corresponding sequence of elementary sounds to be spoken. These elementary sounds are referred to as phonemes. In the frame of speech synthesis, the main usage of a pronunciation model is to generate these phonemes based on an input text. Seeking to integrate expressivity in TTS, we are especially interested in building pronunciation models that can learn or adapt to specic pronunciation patterns and variations. Nonetheless, as already mentioned in introduction, pronunciation modelling is also a problem in ASR. This review will thus not be limited to speech synthesis.

In this section, we rst introduce the general concepts and tasks in pronunciation modelling before explaining the evaluation methodology, then we present the important features to address these tasks. Finally, a review of the major techniques and results from the literature are given.

Overview

Pronunciation modelling can be decomposed into two tasks with their own models. This decomposition is illustrated in Figure 3. The input of pronunciation models are usually words or graphemes and the output are phonemic representations. In sophisticated approaches, extra features can be considered such as part of speech, etymology, etc. Likewise output phonemes can come along with syllables, information about stress, etc. In more details, the rst task consists in converting the input text into its corresponding phonemic representation as it should be considered in the standard language. This phonemic representation will be referred to as canonical pronunciation in the rest of the document. Alternatively the output can be the list or the graph of all possible pronunciations without explicitly determining the one to be chosen. Producing canonical pronunciations is achieved by either searching in a hand-crafted dictionary, or using a Grapheme-To-Phoneme (G2P) converter.

The second task in pronunciation modelling is to modify or rerank the canonical pronunciations in Collection des Publications Internes de l'Irisa c IRISA order to reect a a specic target condition e.g. accented speech, emotion, etc. This task is known as post-lexical processing.

Evaluation methodology

Pronunciation models can be evaluated based on both the generated signal and the generated phonemic representations. As we are more interested in the phonemic level changes in this PhD, we will only consider the evaluation methods and measures for the linguistic side. On the phonemic level, two metrics are mostly used: Phone Error Rate (PER) and Word Error Rate (WER). These metrics are useful to compare the output of a given pronunciation model to a baseline or competing methods [START_REF] Strik | Modeling pronunciation variation for ASR: a survey of the literature[END_REF]. In order to compute these two measures, the generated sequence of phonemes should rst be aligned with the phonemes of a reference pronunciation. Each phoneme is aligned with one or zero phoneme of the other sequence. One of the most widely used string alignment algorithms is the Levenshtein algorithm. This algorithm calculates the number of insertion, deletion and substitution operations needed to transform the reference sequence into the generated one. This determines the so-called edition distance between them [START_REF] Wieling | Evaluating the pairwise string alignment of pronunciations[END_REF].

The result of the alignment process then reveals the phonemes and words which are predicted correctly. Using this information, we can calculate the PER by dividing the number of mispredicted phonemes over the total number of phonemes N :

PER = S + D + I N , (1)
where S, D, and I are the numbers of substitutions, deletions and insertions respectively. When dierent references exist for a same word, only the one with the lowest edition distance is used for PER computation. Calculating WER is almost the same, however words are be taken into account instead of phonemes. WER is frequently higher than PER on a given test set. This is because a word is considered as mispredicted as soon as there is at least one phoneme error.

Besides these two measures, a very similar measure called Accuracy can be used to measure performance of a system. Accuracy measures the correctly predicted units as opposed to error rates [START_REF] Lopes | Phone recognition on the TIMIT database[END_REF]. For instance, the equation for phoneme accuracy is as follows:

Phoneme accuracy = N + S + D + I N = 1 -P ER .

(2)

As for PER and WER, accuracies are expressed as percentages.

Useful features

Pronunciation models, as described previously, handle various types of information as input and output. It is very important to understand these features and to study how they are used within the context of pronunciation modelling. This section describes some of the main features which can be derived from phonemes, syllables, speech signals and linguistics.

Phonemes and phonetic features

Sound units can be divided into two basic types: phones and phonemes. Phones are the basic units which describe any single speech sound with a single articulatory conguration [Taylor, 2009].

Phones are mostly related to the acoustic features found in a particular spoken language, disregarding the phonological role in the language. Phonemes are considered as a more abstract layer of sounds that can be used to represent the linguistic constituents of a language. A single phoneme can represent several phones. For example, in English, the phoneme /p/ has more than one realization such as in the word pit and spit. The /p/ in pit is more aspirated meaning that more air is expelled at the end of the sound [START_REF] Fosler-Lussier ; Fosler-Lussier | Dynamic pronunciation models for automatic speech recognition[END_REF]]. These two dierent realizations are called allophones of /p/. Allophones can be thought as a link between phones and phonemes. In this work, we will

Collection des Publications Internes de l'Irisa c IRISA mostly use phonemes because modelling pronunciation is usually conducted by exploiting linguistic features rather than acoustic features.

Researcher and linguists working in the area of phonology use dierent system for codifying sounds.

One of the most widely used one is called International Phonetic Alphabet (IPA) [International Phonetic Association, 1999]. In IPA, each sound is represented with a symbol and all the sound in any language can be represented using these IPA symbols. Moreover, symbols can be specialized by adding them characteristics (for instance, to dene a phone as stressed or long). This is done by adding special marks called diacritics. A diacritic is a mark added to letters which slightly changes the sound of the letter. For instance, in the French word bonjour, the graphemes on are pronounced as /Õ/, where /O/ is the phoneme and ∼ is the diacritic for nasalization. Having such a standard system of sound representation makes easier working and sharing ideas in this area.

Several types of information can be extracted from phonemes to be used as features in pronunciation models. For instance phonemes can be categorized into vowels and consonants, voiced and unvoiced 1 , nasalized or not, etc.

Syllables and syllabic features

Contrary to what most people think, syllables are not just mere sequences of phones but they are completely distinguishable from phones in the sense that they have structural integrity, and are tightly connected to the higher tiers of linguistic organization [Greenberg, 1999]. The structure of syllables is divided into 3 main parts which are, from left to right, the onset, the nucleus and the coda. The conjunction of the nucleus and the coda forms the rhyme. The nucleus is mandatory and consists of a vowel, while the other two parts are optional and a made of consonants and semi-vowels.

For instance, the word kitten is canonically pronounced /kit@n/. This pronunciation is made of the 2 syllables /ki/ and /t@n/, and the second syllable has the follow structure: the onset is /t/, the nucleus is /@/ and the coda is /n/.

Syllables can also be categorized into open and closed syllables [Moats, 2004]. Open syllables end with a vowel, that is their coda is empty, like in the rst syllable /ki/. At the opposite, closed syllables have phonemes for each of the three parts. Questions arise for closed syllables regarding the segmentation of a word. For example, the phoneme string /kit@n/ could have also been split into the syllables /kit/ and /@n/. Deciding this problem depends on the language while it may also be disambiguated thanks to a spoken example. A syllable can also be stressed or unstressed. Stressed syllables are those with high amount of energy and longer duration. According to [Dilts, 2013], stressed syllables are less likely to be deleted during spontaneous speech. Another factor that leads to variations in speech is the syllable location within a word. As its reported in [START_REF] Vazirnezhad | Hybrid statistical pronunciation models designed to be trained by a medium-size corpus[END_REF], the initial and the middle syllables of words show very low ratios of deletion in spontaneous speech, whereas this ratio is higher in the nal syllable. Lastly, another feature can be derived from syllable: the rate of speech (or speech rate). The rate of speech is counted as the number of linguistic units per second, most of the time syllables per second.

[Fosler-Lussier and Morgan, 1999] reported that when the rate of speech is high, pronunciation of words are more likely to diverge from their canonical forms.

Several studies [Greenberg, 1999, Fosler-Lussier, 1999a[START_REF] Fosler-Lussier ; Fosler-Lussier | Multi-level decision trees for static and dynamic pronunciation models[END_REF]] have suggested that moving toward larger linguistic units such as syllable or word instead of phonemes will improve the performance of pronunciation models. The main idea here is that variations on phonemes are not systematic, leading phoneme-based models to predict too many variants for each phone.

Speech signal features

Using linguistic content to model pronunciation is a widely spread method. At the acoustic level, the pronunciation variants are modelled by adapting acoustic models. In TTS, these models can be used 1 Voiced sounds are those in which the vocal folds vibrate during its articulation, while voiceless sounds are those that the vocal folds do not vibrate.

Collection des Publications Internes de l'Irisa c IRISA Phonology Modelling For Expressive Speech Synthesis: a Review to generate dierent pronunciations. Acoustic models exploit dierent types of features to extract useful information such as F0, pitch and formants and to remove noise from the speech signal.

According to [Taylor, 2009] F0 is the fundamental frequency of a speech signal which is the driving frequency of the vocal cord. Pitch can be explained as the perceived fundamental frequency after undergoing some linearities or errors in the perception. Lastly, formants as described by [Fant, 1971] (cited in [Guilleray, 2012]) are "the spectral peaks of the sound spectrum of the voice", or "an acoustic resonance of the human vocal tract". Formants are extremely important especially in identifying types of vocalic phonemes, i.e. vowels.

Acoustic models represent speech signals with feature vectors such as PLP and MFCC. As reported in [Dave, 2013], each of these feature vectors use a dierent representation of speech signals, for instance, MFCCs is based on the frequency domain and it uses the Mel scale which is based on the human ear scale. Whereas, in PLP, irrelevant information of the speech is discarded.

Linguistic features

Many linguistic features can be derived from words to be phonetized. Though, we only present the 3 most important here.

The rst is the frequency of words in language. Indeed, it is believed that frequent words are easier for listeners to recognize and understand, while rare words are more dicult. However, in reality, speakers tend to use shorter variants for frequent words and pronounce them a bit fast. In contrast, rare words are pronounced more slowly and closer to their canonical forms. That is why frequent words are sometimes less recognizable by speech recognition applications [START_REF] Vazirnezhad | Hybrid statistical pronunciation models designed to be trained by a medium-size corpus[END_REF].

For instance, function words which usually comes at the top of frequent words (articles, auxiliary verbs, etc.) in most languages are mostly shortened during speech [START_REF] Bell | Predictability eects on durations of content and function words in conversational english[END_REF]. Speakers usually use shorter variants of these words which makes it more dicult to be recognized. Studies of large speech corpora have shown that the number of phonemes in frequent words is lower than the infrequent words and deletion of phonemes is higher in frequent words [START_REF] Vazirnezhad | Hybrid statistical pronunciation models designed to be trained by a medium-size corpus[END_REF].

Second, words can show dierent behaviours in speech according to their frequency inside a particular discourse. For example when a word is mentioned for the second time in a discourse, its duration is shorter than the rst occurrence of the word [START_REF] Bell | Eects of disuencies, predictability, and utterance position on word form variation in english conversation[END_REF]. According to [START_REF] Bell | Predictability eects on durations of content and function words in conversational english[END_REF], function words are also short when they are frequent and shorter when they are repeated inside a discourse.

Finally, Part-Of-Speech (POS) can be an indicative feature for pronunciation modelling. POS is the linguistic category of a word such as verb, noun, adjective, etc. [START_REF] Schachter | Parts-of-speech systems[END_REF].

POS is a critical feature of many speech and NLP applications. In some languages like French, POS is extremely important for pronunciation modelling, as it directly aects the pronunciation of some word categories. For instance, the grapheme string ent at the end of third person plural French verbs is silent, e.g. ils parlent, whereas in adverbs like vraiment it is pronounced /Ã/. Moreover, POS is also used in identication of the syntactic and semantic structure of sentences.

Grapheme-to-Phoneme (G2P) conversion

According to [Van Den Bosch and Daelemans, 1993], the objective of grapheme-to-phoneme conversion is to generate a sequence of phonemes for a given word from its spelling. Thus, it generates a sequence of phonemes from a sequence of characters, these characters being called graphemes. The output of G2P can be recomputed by post-lexical processors to further improve the pronunciation or to model variations in speech. An explanation of post-lexical processing can be found later in the next section. while this section focuses on the main G2P techniques, namely knowledge-based and data-driven techniques, with a particular insight of statistical approaches.

Collection des Publications Internes de l'Irisa c IRISA 3.4.1 Knowledge-based techniques G2P converters can be implemented in several ways, but probably the most straightforward one is to store all the possible pronunciations in a pronunciation dictionary and then to look up in this dictionary at run time for each input word. The technique has the disadvantage of not being able to predict the pronunciations of OOVs. In a more exible approach, rule-based techniques are based on the idea that pronunciation of a letter can be predicted from the context of that letter [START_REF] Pathak | The basic grapheme to phoneme (G2P) rules for bodo language[END_REF]. Most of the old rule-based systems consisted of hand-written rules. The drawback of this technique is that it requires experts to craft the rules for each language in order to achieve a good performance. In addition, it might perform very poorly in languages such as English and French where the connection between graphemes and phonemes can be ambiguous [Deshpande, 2013].

Data-driven techniques

Instead of using hand-written rules, data-driven techniques seek to learn the rule automatically from examples and apply them accordingly. Neural networks and analogy learning are the most widely known machine learning techniques for data-driven G2P conversion. Neural networks is a classication approach which predicts each phoneme independently by only taking into account the context of the current grapheme [Jiampojamarn, 2011]. One of the rst examples of using neural networks in bulding grapheme-to-phoneme systems is the NETtalk system [START_REF] Sejnowski | Parallel networks that learn to pronounce english text[END_REF] (cited by [Taylor, 2009]). NETtalk consisted of 3 layers. The input layer was made of 203 neurons, the hidden layer of 80 and the output 26 units coding the phoneme to be produced. It considered only seven characters at a time with a window of three characters from right and left of the target character. The input and output of the system were encoded with various features (voiced, stress, syllable boundary, etc.).

The idea behind pronunciation by analogy comes from the studies of how humans learn the pronunciation of new words. When a human is given a new word, he/she learns its pronunciation by comparing it to the nearest known words and adapting or combining their pronunciations [Taylor, 2009, Dedina and[START_REF] Dedina | [END_REF]. For instance, if we consider the word fax as our target new word, a human would automatically think of a similar word such as tax and adapt its pronunciation.

Pronunciation by analogy algorithms work by comparing substrings of the unknown word to those extracted from the pronunciation dictionary and nd the closest match [START_REF] Damper | Pronunciation by analogy: Impact of implementational choices on performance[END_REF].

Statistical techniques

The statistical approach is more recent compared to the other two techniques. It includes models such as Hidden Markov Models (HMM), Conditional Random Fields (CRFs) and joint n-gram models.

In HMMs, the model is allowed to use the previously predicted phonemes for the future decisions. Phonemes are represented as states of a Markov chain and linked to to their most likely corresponding graphemes [Karanasou, 2013]. The Viterbi algorithm is used to predict the optimal state sequence [Viterbi, 1967]. An example of using HMM in G2P is the work of [Taylor, 2005] in which he suggests that HMMs alone are not sucient for G2P modelling but by adding a preprocessing step they can be improved. The preprocessing step rewrites some of the graphemes and rearrange them. For instance, a word like hate would be rearranged to haet and graphemes x were rewritten as ks.

On the other hand, CRFs are also probabilistic models used for labelling sequential data. CRFs are widely used in NLP to solve sequential problems such as POS tagging [START_REF] Tellier | Pos-tagging for oral texts with crf and category decomposition[END_REF],

G2P [Illina et al., 2011, Wang andKing, 2011], etc. CRFs oer several advantages over HHMs by relaxing the strong independence assumptions [START_REF] Laerty | Conditional random elds: Probabilistic models for segmenting and labeling sequence data[END_REF]. CRFs compute output probabilities Pr( y| x) of a sequence of observations y = (y 1 , . . . , y n ) from a sequence of in-Collection des Publications Internes de l'Irisa c IRISA put x = (x 1 , . . . , x n ). The most important part of CRFs are the so-called feature functions.

When used in a task like G2P conversion, each feature function takes as input a grapheme that we want to convert to its phonemic representation, and several types of information about the grapheme, such as the word it belongs to, the position of the grapheme in the word, the POS of the word, and the surrounding graphemes. These features are then given weights using techniques like gradient ascent. The features and their respective weights are then used to nd the optimal sequence using dynamic programming algorithms like Viterbi [START_REF] Sutton | An introduction to conditional random elds for relational learning[END_REF].

Lastly, joint n-gram models use substring pairs of graphemes and phonemes so that the information about both part can be exploited [Jiampojamarn, 2011]. The graphemes and phonemes are rst aligned so that each grapheme corresponds to its phoneme, using a Dynamic Time Wrapping (DTW) algorithm [START_REF] Pagel | Letter to sound rules for accented lexicon compression[END_REF]]. Joint n-gram models can have orders ranging from 1 to 7.

At run time, a simple search through the pairs would give the most probable sequence using the Viterbi algorithm again [Taylor, 2009].

Post-lexical processing

The results of G2P converters can be further processed to modify the generated pronunciations.

The goal of post-lexical processing can be to improve the pronunciation or to model pronunciation for a given target expressivity. In this section, the main works in this area are reviewed. [Miller, 1998] studied post-lexical phonology, which can lead to interspeaker variations, using neural networks. In order to predict the post-lexical pronunciation, the canonical pronunciations were encoded along with prosodic information and then fed into a neural network. Context of the phonemes were also fed into the neural network by using a window of three phonemes (one from left and one from right). For each target phoneme, the neural network outputted a post-lexical phoneme, a silence for deletions, or a diacritic to indicate minor changes in the pronunciation of the canonical phoneme. The system performed best when the variants of a phoneme were few, such as in case of word-initial vowel glottalization 2 , where only two variants are available. However the systems struggled when the number of variants were more than two, such as the phoneme /t/.

In another study, [START_REF] Vazirnezhad | Hybrid statistical pronunciation models designed to be trained by a medium-size corpus[END_REF] followed a dierent technique which consisted of a decision tree and a contextual rule generator to produce post-lexical pronunciations. Given an input phoneme string, the decision tree was used to predict the phonemes that needed to be changed, while the contextual rules module was used to generate the post-lexical changes such as substitution, insertion or deletion of phonemes that were susceptible to change. The features that the authors included in the decision tree were rate of speech, word unigram probabilities, syllable location, and word stress. These features are known to have a huge impact on pronunciation variation in spontaneous speech. The authors compared their system to a baseline system which used only phonemic version of the words without using any of the aforementioned features. Their system achieved the best result when the lexicon contained 2.61 variants per word with 48% WER compared to the baseline system which had 54% WER. This shows that using extra features in addition to the sole phonemes is useful for post-lexical processing. [Jande, 2003] studied how speech rate and speaking style aects pronunciation and phone-level reduction 3 in Swedish. The goal was to capture the general pronunciation variations in spontaneous speech rather than individual or dialect-related variations. Several rules were extracted to conduct the analysis such as haplology 4 , forward and backward assimilation 5 , and elision of the important phonemes such as /r/ and /h/. Common words matching these rules were then extracted, and 2 Glottalization is the closure of vocal folds during the articulation of a sound.

3 Phone-level reduction occurs when a word is uttered without pronouncing all the phonemes that it contains. Reduced words can still be understood. It exists mostly in spontaneous speech. 4 Haplology is the deletion of successive identical syllables or consonant sound groups. For instance, the word library which has a canonical pronunciation of /laI.br@r.i/ is pronounced as /laI.bri/ in spontaneous speech.

5 Assimilation rules transfer a phonological feature or a set of features from a segment in a phonological string to the succeeding segment. For instance, the word bags in English is pronounced as /baegz/, and the /s/ is pronounced as /z/.

Collection des Publications Internes de l'Irisa c IRISA their realized post-lexical forms were compared to non-reduced (canonical) ones by presenting both to listeners in test utterances. The result of this evaluation showed that the canonical forms were considered more natural when the speech rate is low, while reduced forms were judged as the most natural when the speaking rate was medium or high.

Lastly, [START_REF] Bennett | Using acoustic models to choose pronunciation variations for synthetic voices[END_REF] tried to mimic an individual speaker by predicting a speaker's choice of pronunciation between reduced forms and full forms of English words. The focus was on the most common words which are known to have multiple pronunciations. For instance, the English words the, a, to, and for can have dierent pronunciations based on their context. One of the best known cases is the pronunciation of the which is mostly pronounced as /ð@/ when it is followed by a consonant-initial word and is pronounced as /ði/ when followed by a vowel-initial word. However, exceptions occur in many situations. For instance it might be pronounced as /ði/ even before consonant-initial words. For instance, when uttering the phrase the car in a context where the mentioned car is meant to be unique in some sense. The evaluation results on the words showed that the prediction for some of the words like for and a were mostly correct, while it failed to capture the variations in pronunciation of the other two words especially to.

Its very important to understand all the tasks and components which take place in pronunciation modelling and the way data is processed in each component. Therefore, this section presented a general overview of pronunciation modelling and the most important concepts in this area (G2P, post-lexical processing, features, etc.). In the next section another important area of phonology modelling will be discussed: disuencies.

Disuencies

One of the main dierences between neutral speech and expressive speech is that the latter contains lots of disuencies. Speech disuencies are generally dened as phenomena that interrupt the ow of speech and do not add propositional contents to an utterance [Tree, 1995]. Disuencies were considered as irregular phrases by most researchers and therefore had received very little attention from the researchers working in the area of phonology modelling. However, some studies have shown that there are actually remarkable regularities and patterns in disuencies [Shriberg, 1994]. These regularities can be used to model disuencies in order to improve expressive speech modelling.

Among researchers working in the area of disuencies, there is an agreement on the structure of the surface form of disuencies, that is what can be observed from them in a spoken utterance. [Shriberg, 1994] suggests some standard terms for the regions of disuencies which is as in Figure 4. The section called Reparandum (RM) refers to the part of the linguistic message that will be deleted. Some researchers have preferred to refer RM to only the mistakenly uttered word such as "boston" in the above example as supposed to the entire deleted section. The Interruption Point (IP) is the exact place in which interruption occurs. That is when the speaker detects a trouble in his speech. The next section is Interregnum (IM) and refers to the section which is an indicator to the start of an editing phase or correction phase. Finally, Repair (RR) is the section in which the speaker corrects his/her speech.

Disuencies can change form by language, but generally there are some accepted types which can be found in most languages. According to [START_REF] Stolcke | Statistical language modeling for speech disuencies[END_REF] the main disuency types are:

• Filled pauses (FP): includes llers like uh and um.

• Repetitions (REP): repeated words are considered as disuencies, such as "the the word".

• Deletions (DEL): words without any correspondence such as "I... did you happen to see.

In this section, we will highlight the usage of some disuency types and the possible positions in which they might appear.

Collection des Publications Internes de l'Irisa c IRISA Figure 4: Terminology for disuency regions (source: [Shriberg, 1994]) 4.1 Usage and functions of disuencies Each of the above mentioned disuency types have dierent functions and are used for dierent purposes. For example uh and um which by some researchers are considered to be silent pauses but lled without conveying any meaning [Eisler, 1968]. On the other hand, other researchers see these two disuency types as lled pauses which are used to indicate the beginning of a delay that speakers use to search for a phrase and keep their conversation going on [START_REF] Clark | Using< i> uh</i> and< i> um</i> in spontaneous speaking[END_REF].

Another pair of disuencies that have similar characteristics but sometimes used for dierent purposes are you know and I mean. According to [Fox Tree and Schrock, 2002], these two markers have three basic meanings. The rst is that these markers provide information about the speaker, including anxiety, uncertainty or lack of self condence. They can also be an indicator of the speaker group or social class. The second proposal suggests that they are indicators for dierent situations such as informality or amusement. A great deal of these markers are found in informal speech and only few of them in formal speech. The nal meaning is that they are used to express shared understanding on a topic, usually called positive politeness. This helps decrease the social distance between the speakers and makes speech more casual.

On the functions of the discourse marker oh, [Fox Tree and Schrock, 1999] points out that the function of oh might change based on the place it is found. However generally this discourse marker has functions like a sudden reaction to new or surprising information, a signal of an upcoming repair, and to demonstrate the speaker's engagement in the conversation (this is also sometimes referred to as backchannels). In addition oh signals an incoming separate piece of information that should be treated independently from the previous information, thus it helps listeners to understand more easily.

Regarding repetitions, they are considered as a sequence of processes that can be divided into four stages [START_REF] Clark | Repeating words in spontaneous speech[END_REF]]. In the rst stage, the speaker makes the commitment to utter a phrase, and initiate it by saying the rst word. In the second stage which occurs after the rst word, the speaker suspends its speech because of dierent reasons such as thinking about reformulating his/her speech or cleaning throat. The third stage is between the suspension and the resumption point where the speaker utters a lled pause such as uh or remains silent. Lastly the speaker switched to what [Shriberg, 1994] calls repair and, in case of repetitions, it involves repeating the rst word and then the correct phrase such as: "I uh I want to...". As for the function of repetitions, [Shriberg, 1994] reports they serve the smoothing process after a long pause.

Collection des Publications Internes de l'Irisa c IRISA

Position of disuencies

Disuencies occur at dierent positions in sentence or more specically at dierent positions of intonation units. The ratio of disuencies might change based on the position and how much planning the speaker have done before the intonation unit. An analysis of the positions of uh and um has revealed three locations in the content of an utterance where these llers usually appear [START_REF] Clark | Using< i> uh</i> and< i> um</i> in spontaneous speaking[END_REF]]. These locations are (i) at the boundary, (ii) after the rst word, and (iii) at later positions of the intonation unit. Among these three locations, planning the speech is the most dicult at position (i), thus these llers appear the most in this location. Logically, planning the speech is easier at (ii) and (iii), and less llers appear there. The rate of occurrences of all disuency types generally can be related to the level of planning of the speaker as pointed out by [START_REF] Bortfeld | Disuency rates in conversation: Eects of age, relationship, topic, role, and gender[END_REF], therefore these three positions can be generalized and applied to all other disuencies.

In another experiment, [Swerts, 1998] analysed the distribution of lled pauses at dierent discourse boundaries 6 . The results showed that 78% of the phrases following a strong boundary had lled pauses and only 40% of the phrases following a weak boundary contained lled pauses. In addition, the lled pauses that follow a strong boundary mostly occur in initial position. Besides, the study showed that the existence of a boundary makes hesitations more likely. This nding is consistent with [START_REF] Bell | Eects of disuencies, predictability, and utterance position on word form variation in english conversation[END_REF], suggesting that a large number of disuencies occur at initial positions of an utterance.

Disuencies have been considered as elements making the speech more dicult to comprehend for a long time. However some studies have reported that disuencies actually help listeners to comprehend easier in many cases [Brennan andSchober, 2001, Fox Tree andSchrock, 1999]. This shows that studying disuencies and understanding them can lead us to better model phonology and produce more natural and comprehensible synthetic speech utterances.

Conclusion

In this report, we reviewed expressivity and how it aects the variations in phonology. Expressivity is one of the most important factors that makes human speech natural. The three main declinations of expressivity are emotion, speaking style, and intention. They are known to have eects on phonology, i.e pronunciation and disuencies. Expressivity can aect the acoustic side of speech, however in this study we only considered the linguistic eects of expressivity. Mainly, we discussed the area of pronunciation modelling which, in general, deals with nding the corresponding phonemic representations of a given text. Pronunciation modelling can also be adapted to model specic pronunciation patterns, variations or styles. The two respective key subtasks for this are G2P conversion and post-lexical processing. Pronunciation models can work with several types of input units like phonemes, syllables, and speech signals. Each of these units has its own pros and cons.

Finally, disuencies, which are an important characteristic of expressive speech, were discussed.

Although disuencies were considered as irregular events for a long time, some researchers have found regular patterns in disuencies. These regularities can help us model disuencies and to have better integration of disuencies in phonology models.

The rst step towards working on this subject will be extracting and analysing the characteristics of expressivity in speech corpora. As a preliminary work, we have analysed a spontaneous speech corpus named the Buckeye corpus and extracted some statistics about characteristics of spontaneous speech. The extracted information from the corpus conrms some of the ndings of papers from this bibliographical review, such as the high ratio of phoneme deletion in the nal syllables of 6 A phrase is considered to be a discourse boundary if it can separate two pieces of information in the preceding and the following phrases. The degree of separation determines if a boundary is strong or weak. In cases where boundaries are determined by human evaluators, boundaries are said to be strong if the inter-annotator agreement is high, whereas the boundary is weak if there is a doubt about its presence.

Collection des Publications Internes de l'Irisa c IRISA Phonology Modelling For Expressive Speech Synthesis: a Review words, and the reduction of phonemes in the frequent words. In the next step, we will try to build models that can learn the characteristics of expressive speech and rules which lead to variations in expressive speech, e.g, spontaneous speech. As an example, the model might learn rules such as the transformation of /t/ → /P/ 7 as in the word that. Next, we will try to integrate the model in a TTS system to generate expressive speech. Integrating such models in TTS might be more challenging than in ASR, because in ASR, the system might contain several alternative pronunciations of the same word without ranking them. Whereas in TTS the system has to generate one single output for each word, and in case of having multiple alternative pronunciations for the same word, they have to be ranked to determine the best one. Later, we will move to another important subject which is accents. To do so, rst, we have to analyse an accented speech corpus, and then transfer our knowledge that we learnt before to accented speeches. Finally, in the last year of the PhD, disuencies will be studied. The eld of disuency is a very challenging eld, and it has been very poorly studied until now, especially in the domain of TTS.

  phonologie pour la synthèse de parole expressive Résumé :

Figure 1 :

 1 Figure 1: Architecture of (a) TTS and (b) ASR systems

Figure 2 :

 2 Figure2: 2-dimensional representation of emotions (source:[Russell, 1980])

Raheel Qader, Gwénolé Lecorvé, Damien Lolive, Pascale Sébillot


Estelle Malavolti
email: estelle.malavolti@enac.fr.

Single Till or Dual Till at airports: a Two-Sided Market Analysis

Keywords: two-sided market, network externalities, air transport economics. JEL codes: L11, L12, L89

Big airports profits are more and more often coming from commercial activities such as retailing. However, commercial services are relatively far from the original mission of the airport: providing airlines with aviation services such as ground handling, terminal management or airside operations, and being regulated for that because of an obvious dominant position with respect to airlines. For this reason, one can advocate for the separation of the two activities, i.e. for a dual till approach, in which only the aeronautical activity is regulated. We, instead, suggest that a single till regulation, in which the total profit of the airport is examined, is relevant because it allows to take into account the externalities existing between retailing and aeronautical services.

, 2006), we show that the airport is a platform which makes the shops and the passengers meet.

The retailing activity depends on how many passengers are circulating and connecting at the airport, as well as the time they spent in the airport, while passengers value the least connecting time as possible. We show that the aeronautical tax can be either higher or lower under single till depending on whether the impact of the passengers demand or of the waiting time is the more important for the shops.

Introduction

The commercial activity of big airports is becoming more and more important: The share of the commercial profits in their total profits has increased a lot. It represents 60% of the profits for Fraport, Frankfort airport, meaning that it is more important than the core activity of the airport: providing airlines with aeronautical services. Commercial revenues increased by 9% for the now privatized Aeroports de Paris. In 2007, the commercial activity accounted for 26% of Schiphol Group (Amsterdam)'s revenues and 34% of the operating result.

The investment strategies of airports are thus taking into account this aspect: when deciding to extend the capacity of an airport (by building new terminals for example), airport managers include the space for new shops. For instance, the extention of Beijing airport, which surface represents 1.3 million square meters, which stands for 1.6 times the surface of the original terminal, while the number of passengers is supposed to double (in the short run).

However, commercial services are relatively far from the original mission of an airport: providing airlines with aviation services such as ground handling, terminal management or airside operations, and being regulated for that because of an obvious dominant position.

How should airports manage both the aeronautical and the commercial activities? Should we separate the two activities? Are the kind of questions we address in this paper.

Our paper offers an original interpretation of the problem with the use of two-sided market. The airport is indeed a platform which makes passengers and shops meet. Shops are interested in having passengers wandering in the airport while waiting for a connecting flight. They will be more willing to pay for a space at the airport if there are a lot of passengers travelling and if they are in connection and wait sufficiently for this connection.

Then the airport could be tempted to decrease the passenger tax in order to make people travel more. However there exists a side effect on passengers demand: The airline could choose a too high waiting time caused by a low aeronautical tax, and thus make passengers travel less. We show that if the airport consider the two activities as being related it de facto internalizes effects which are complex and playing in different directions. We show that if the externality on passengers is high enough, the aeronautical tax is set at a lower level: Passengers are subsidized to travel, i.e., they pay a lower ticket price and wait less, by shops, which pay a higher rent for the space. On the contrary, if the marginal impact of the waiting time on shops demand is high enough, the aeronautical tax is set at a higher level: Less passengers travel and they wait more, which allows the airport to make more profit on the shops side.

Our paper relates to the economics of media markets as well as to the literature on two-sided markets. [START_REF] Rochet | Two-Sided Markets: A Progress Report[END_REF] attempt to build a general framework for two-sided markets and give a definition: A market is said to be two-sided when the volume of transactions on both sides is affected by a change in the price of one side of the market, keeping the total price constant. This means that the price structure affects the profits and the economic efficiency1 . The literature on two-sided markets builds on two branches of the literature: Firstly, the literature on network externalities (Katz andShapiro (1985,1994), [START_REF] Farrell | Standardisation, Compatibility and Innovation[END_REF]) and more specifically on indirect externalities (e.g. [START_REF] Chou | Network effects without Network Externalities[END_REF]) and secondly the literature on multi-product pricing. In our paper, externalities are present in that shops are both interested in having more passengers and having them waiting a long time for their connection. However, intermediaries are needed in this context because passengers do not internalize their positive impact on retailers2 . As a consequence, the price structure matters, which is not considered in the classical network externalities literature. On the contrary, the literature on multi-product pricing focuses on price structure but forgets about externalities. Because the sides of the market need one each other to exist, the problem can indeed be considered as a problem of pricing in the case of complementary goods: If the price of the ticket decreases, the demand for space increases. However, this is forgetting about the externality exerted by the shops on consumers, through their sensitivity with respect to the connecting time. 3 .

The media industry is one of the first application of two-sided market: viewers want to watch programs and dislike the announcements they carry, whereas advertisers see audience as potential consumers 4 . Generally, what authors show is that it makes sense that advertisers subsidize the TV consumers because of the presence of externalities. Our paper builds on this literature in a sense but the application is completely different. We use a classical framework as presented in [START_REF] Rochet | Two-Sided Markets: A Progress Report[END_REF] with usage externalities: the retailers are sensitive to the number of passengers wandering in the airport. To the difference to [START_REF] Rochet | Platform Competition in Two-Sided Markets[END_REF] or [START_REF] Armstrong | Competition in Two-Sided Markets[END_REF], we do not model competition between platforms, as an airport is de facto in a monopolist situation with respect to airlines and shops, but fully model the consumers side as in Crampes et alii (2006). Besides we model the fact that airlines choose nonetheless the ticket price but also the connecting time for passengers. This allows to take into account a side effect of the presence of shops: They are interested by having more passengers, i.e. passengers demand exert a positive externality on shops. However, shops are also interested in the time spent by these passengers in the airport: The more the waiting time, the more the shops demand.

This may lead the airport to try to increase the waiting, creating a negative externality on passengers.

The paper is organized as follows: Section 2 sets out the model and derive the general results while in Section 3, we discuss a numerical example. Section 4 concludes and provide some insights in terms of welfare analysis5 .

A two-sided market model

Airports are "economic catalysts" as they have "two groups of customers who need each other in some way; but who can't capture the value from their mutual attraction on their own; and rely on the catalyst to facilitate value-creating reactions between them" (Evans and Schmalensee 2007). According to [START_REF] Evans | Catalyst Code[END_REF], catalysts do exist for a while but will play an increasingly important role in our economies due to technological changes and the reduction of the communication costs. There are several examples of catalysts, for instance, Rochet and Tirole (2004) mentionned Videogame platforms, which need to attract gamers in order to convince game developers to design games to their platform and need games in order to induce gamers to buy and use their videogame console; payment card systems, which need to attract both merchants and cardholders; TV networks, portals, newspapers, which compete for advertisers as well as audience.

An airport plays the role of a platform which makes passengers and shops meet. Shops need to be present at the airport to reach passengers. Shops will address their demand directly to the airport. To contrast, passengers buy tickets by an airline, which decides of both a ticket price and a connecting time. The airline has to pay an aeronautical tax set by the airport. Finally, the airport chooses the rent for the space and the level of the aeronautical tax, up to a certain level (it is regulated by a price cap) 6 .

The Aeronautical Activity

Consider would-be passengers who express a (total) demand for travel N (p, t). It is function of the price of the ticket p, which is set by the airline and of the connecting time t.

We assume that demand is decreasing in the price p and in the connecting time t, and that the cross derivative is negative

δ 2 N (p, t) δpδt < 0
This assumption is made to take into account that the price of the ticket and the connecting time are imperfect substitutes for passengers: I may accept to wait a longer time if the price is really low. On the contrary, if the price is high, I tolerate it only if the connecting time is very low as well.

We consider an airline in a monopolist situation because in hub airport one airline is often in a dominant position. The airline takes as given the aeronautical tax a imposed by the airport. This tax is proportional to the number of passengers N (p, t). The airline sets both the price of the ticket which will be paid by the consumers and the connecting time, i.e.. the time spent by passengers in the airport between two connecting flights.

The connecting time t has no price as such but allows the airline to save some production costs. Given C(N, t) the production cost, we then assume that C(N, t) δN ≥ 0 and that C(N, t) δt ≤ 0. The program of the airline is thus as follows

M ax {p,t} Π = (p -a)N (p, t) -C(N, t)
The first order conditions then gives the following equations:

δΠ δp = 0 ⇔ p -a -δC δN p = 1 ǫ N/p (1) δΠ δt = 0 ⇔ p -a -δC δN = δC δt / δN δt (2)
Equation ( 1) tells us that the monopolist mark-up of the airline has to be equal to the inverse of the direct price elasticity, denoted by ǫ N/p , which is a classical result. More interestingly, the second equation explains that the difference between the price and the cost (which includes variable t) is function of the gain in terms of cost by an increase in the connecting time, measured by δC δt and of its cost in terms of demand. When computing the ratio (1)/(2), we obtain the following expression:

p = ǫ N/p (- δC δt δN δt )
The couple (p, t) in determined such that the price of the ticket equals an expression which stands for the monopolist trade-off between saving costs when increasing t and loosing passengers because of a higher connecting time, weighted by the the direct elasticity of the demand with the price. An explicit solution for the price and the connecting time is expressed in the next section.

The monopolist internalizes the fact that the connecting time influences the demand and the price and the connecting time are imperfect substitutes to serve a certain level of demand. On the contrary, the airline forgets that it has an influence on the aeronautical tax through the choice of t. The airport, playing its role of platform, is the one who will internalize the effect.

The Commercial Activity

Shops are present in the airport. They are numerous and in competition (perfect) for the occupation of the space in the airport. They express a demand which is naturally decreasing in the rent r paid to occupy the space. Their demand is also function of the number of passengers who wander in the airport as well as of the connecting time of these passengers. Indeed, the more number of passengers and the more likely the sell. However, the sell is also explained by the time passengers spend in the airport, waiting for their next plane. Thus, demand for space from shops is decreasing in the price r and increasing in t and N . From the shops point of view, they are interested in fact by a mix between passengers and having them waiting sufficiently longer in the airport. The connecting time and the passengers are imperfect substitutes for the retailers. We define s the demand for space from shops. s has the following characteristics:s = s(r, N, t) with, for all r, N , t

δs δr < 0 δs δN ≥ 0 δs δt ≥ 0.

The Platform

The airport is a platform which will make the link between both the commercial and the aeronautical activities. It will set both the aeronautical tax a and the space rent r in order to maximize the joint profit of the two activities. We assume that the (production) cost of the airport is linked to the demand of passengers (and not chargeable to each of the activity). To make things simpler, we further assume that these costs are proportional to passengers demand (parameter γ, with γ > 0). We consider fixed cost and denote them CF . The program of the airport can thus be written

M ax {a} Π airport = aN +rs -γN -CF s.t. s = s(r, N, t) , N = N (p, t) , p = p(a) , t = t(a) .
The FOC, taking into account the constraints,i.e. considering that N (.) is a function of a, write If the shops demand is sensitive to the rent, the level of the rent will be naturally lower.

The level of a is determined so as to take into account several effects: the first effect, N (a)-(a-γ)N ′ (a), corresponds to the impact of a on the pricing of the ticket. Indeed, increasing a will have an impact on the choice of the airline (p, t). If the airport were considering independently the two activities, this effect would be the only one present to determine a, i.e. the impact of t on passengers demand would have been the sole impact taken into account. The second impact, rN ′ (a) δs δN , measures the externality exerted by passengers demand on shops activities but weighted by the indirect impact of the aeronautical tax on the passengers demand. The sign of this effect depends on how passengers demand reacts to a. The last effect, rt ′ (a) δs δt , takes into account the impact of the connecting time t on shops profit. The sign of this last effect depends on the impact of the aeronautical tax on the waiting time. To measure the total effect and determine whether the aeronautical tax a is lower or higher than with a situation in which the airport considers independently the two activities, one need to determine the impact of the tax on the ticket price and on the connecting time. a is part of the marginal cost of the airline. As such, as the mark-up ( p-a-δC δN p is the margin above the marginal cost (represented by δC δN ), the ticket price p should be increasing with the aeronautical tax, i.e., p ′ (a) ≥ 0. The connecting time t is a substitute to the ticket price to satisfy the passengers demand, as such, the aeronautical tax a should have the same impact, i.e., t ′ (a) ≥ 0. Hence, both the ticket price and the waiting time are increasing with the aeronautical tax. As the passengers demand is assumed to be decreasing in both the waiting time and the ticket price, we conclude that it is decreasing with the aeronautical tax, i.e., N ′ (a) ≤ 0. We can then re-interpret the first order conditions. Now that N ′ (a) ≤ 0 and knowing that the first part of the FOC, i.e., N (a) -(aγ)N ′ (a) is monotonically decreasing in a, adding rN ′ (a) δs δN which is a negative term (for all a and r) means that the solution in a should be lower than if the two activities were considered independently. Since passengers demand is affected negatively by a change in the aeronautical tax, increasing the tax means having less passengers, which means having less demand for space too. The sign of the last effect, measured by rt ′ (a) δs δt , is opposite. Indeed, t is increasing in a, so as the effect of the connecting time on the space demand δs δt . Then, rt ′ (a) δs δt is positive for all a and r. Comparing with a situation in which the commercial and aeronautical activities are independent, this effect tends to increase the level of aeronautical tax. Since the connecting time is positively affected by the aeronautical tax, increasing the tax means having a higher connecting time chosen by the airline, which in turn means having more demand from shops. We thus cannot conclude on the global effect, i.e.., on the choice of the aeronautical tax by the airport.

The aeronautical tax tends to be lower if the (negative) effect on passengers demand is high enough. It is higher if the effect on the connecting time is high enough. To conclude on the effect, on need to give expression for both the passengers and the shops demands.

The choice of a has an impact on the choice of r through the shops demand. If the twosided aeronautical tax is lower, this means that the impact of a on the shops demand is negative. Indeed ds da = N ′ (a) δs δN + t ′ (a) δs δt .

The demand for shops being decreasing with a, the price for space is higher in the twosided market situation. The aeronautical tax and the rent are impacted differently by the two-sidedness of the market.

We sum up these results in the following proposition:

Proposition 1
The aeronautical tax a is set lower and the rent r is set higher in the case of two-sided market if the partial impact of passengers demand N on shops demand s is more important than the partial impact of the connecting time t on shops demand s.

The airport thus internalizes the two contradictory effects when choosing its prices.

To be able to measure the effects, let us consider a numerical (simple) example.

Numerical example

Let us define specific functions for our problem. For example, we define passengers demand function as follows

N (p, t) = ū -p -αt -βtp.
where ū is the net utility derived if the consumers do not travel, we normalize it to unity.

Parameter α measures the direct impact of the connecting time on passengers utility. We assume that this impact is lower than the one of the direct price, i.e. α < 1. Parameter β measures the cross effect between p and t for the passengers. β is positive to take into account the fact that if the waiting time (respectively the ticket price) is high, the marginal impact of the ticket price (resp. the waiting time) on passengers demand is even higher in absolute value. Linearity is assumed to obtained simple results.

We interpret the role of the connecting time as a means for the airline to decrease its marginal cost. The cost of producing travel C(N, t) is for example chosen to be as follows

C(N, t) = (c -t)N.
Where c > 0 is the unit cost.

The demand for space is expressed as follows:

s(N, t, r) = κN + λtr.

Let us now solve for the equilibrium values of p, t, a and r, with the corresponding quantities N and s. Solving first the airline program allows to state the following lemma.

Lemma 1 The difference between the two instruments p and t available to the airline is constant

p -t = 1 -α β Proof.
From the FOC of the airline we obtain that

t p = ǫ N/t ǫ N/p .
Which simplified to the following expression

p -t = 1 -α β .
Lemma 3 Under our assumptions, the aeronautical tax is lower if the airport considers the two sides of the market a T S < a 0 .

Proof.

Considering the FOC on a, what matters is the sign of ds/da. Computing ds/da leads to the following expression:

-8α(1 + β)κ -(-B + p B 2 + A)(-Bκ -λ),
where B = 1 -ac and A = 16α(1 + β). A > 0, while we cannot conclude for B since a is endogenous.

In the case B is positive, then the global expression is negative, thus ds/da < 0, implying that a T S < a 0 .

If B < 0, but λ is sufficiently important, then the global effect is also negative.

The aeronautical tax being lower when the market is considered to be two-sided, we can now derive the impact on the other equilibrium variables. Indeed, as the ticket price and the connecting time are increasing in a, p T S < p 0 and t T S < t 0 , implying that more passengers travel at the equilibrium. The shops demand is lower, because ds/da < 0, and, from the first order conditions, shops pay a higher rent.

Conclusion

The airport is a platform which takes into account the externalities existing between the commercial activity and the aeronautical activity. As shops are sensitive to both the waiting time and the number of passengers present at the airport, two contradictory effects have been determined: the aeronautical tax is lower if the shops are more sensitive to the number of passengers. We conclude as well that separating the two activities, i.e. considering the double till regulation, is synonymous of forgetting the externalities potentially existing between the two sides of the market. What we aim to value now is to try to estimate empirically if there are some externalities, and, if so, what effect is the most important on shops demand.

δΠ airport δa = 0 4 )

 04 ⇔ N (a) -(aγ)N ′ (a) +rN ′ (a) δs δN +rt ′ (a) δs δt = 0 (3) Where t ′ (a) (respectively N ′ (a) denotes the total derivative of the waiting time (resp. the passengers demand) with respect to the passenger tax a. Equation (4) can be rewritten as follows r = -s δsδr .

The paper by[START_REF] Baxter | Bank Interchange of Transactional Paper: Legal and Economic Perspectives[END_REF] first introduced the notion of interdependence of demands for an antitrust case concerning banks interchange fees.[START_REF] Armstrong | Competition in Two-Sided Markets[END_REF] and Parker and Van Alstyne (2005) are general papers which set out the notion of two-sided markets and derive general results. Evans and Schmalensee (2007) give a practical description for two-sided markets and a lot of examples of multi-sided businesses.

[START_REF] Caillaud | Chicken and Egg: Competition among Intermediation Service Providers[END_REF] study the role of intermediaries when there are indirect externalities

For an explanation of the price theory of two-sided markets, see[START_REF] Rochet | Two-Sided Markets: A Progress Report[END_REF] and[START_REF] Weyl | The Price Theory of Two-sided markets[END_REF].

See Anderson and Gabszewicz (2005) and Evans and Schmalensee (2007) for a detailed review. Other interesting papers are Gabszewicz, Laussel and Sonnac (2004) for an analysis of advertising under free-toair, or Peitz and Valletti (2007) for an analysis of the advertising intensity and the content programming of free-to-air and pay-tv. Crampes, Haritchabalet and Jullien (2006) model endogenous entry in a model where platform compete for advertising resources

.[START_REF] Baxter | Bank Interchange of Transactional Paper: Legal and Economic Perspectives[END_REF] For general analysis of welfare in two-sided markets, see for instance[START_REF] Anderson | Market provision of Public goods: The case of broadcasting[END_REF] or Ambrus and Reisinger (2005) for a specific analysis of media market. Nocke,[START_REF] Nocke | Platform Ownership[END_REF] focuses on platform ownership and find that if network externalities are important, a monopolistic platform is socially preferred.

We do not model the regulator as such. We left this for further research.

The difference between the price of the ticket and the connecting time is held constant by the airline because of the linearity of the demand essentially. It is nevertheless interesting to notice that the more the cross effect between the two instruments (measured by β) and the less the difference, while the more the direct impact (measured by 1 -α), the more the difference. It is interesting to notice that the impact of the aeronautical tax is identical for both instruments dp da = dt da .

Solving for the first order conditions stated in the previous section we obtain the following expressions for the price of the ticket, the connecting time and the number of passengers at the equilibrium:

Lemma 2 At the equilibrium, the ticket price p T S and the connecting time t T S varies positively with respect to the aeronautical tax. Passengers demand N T S varies negatively w.r.t. the aeronautical tax.

Proof.

When derivating p T S w.r.t. a, one obtains that it depends on the sign of

Two cases have to be considered. If a ≥ 1 -c, then the ticket price is increasing with a (if supposedly, c < 1). On the contrary, if a < 1 -c, then the expression has the following form:

, where A = 16α(1 + β) > 0 and B = (1 -ac)β > 0 and we can directly conclude that it is always positive (for all a). We conclude that p is increasing in a, so as to t. As N (p, t) is decreasing w.r.t. both t and p, then it is decreasing in a.

If the aeronautical tax is set at a lower level, we can conclude that the ticket price and the connecting time are lower than if the activities were treated separately. At the equilibrium, the number of passengers is higher: More people travel.


M Collet

M Ouisse

Integrated and Distributed Adaptive Metacomposites for vibroacoustic control of Aerospace Structures

Research activities in smart materials and structures represent a significant potential for technological innovation in mechanics and electronics. The necessity of controlling vibroacoustic behavior of industrial systems motivates a broad research effort for introducing active or passive technologies to control noise and vibrations. New processes are now available which allow active transducers and their driving electronics to be directly integrated into otherwise passive structures. This new approach could allow fine control of the material physical behavior for implementing new functional properties that do not exist in nature. In this sense, we can speak of "integrated distributed adaptive metacomposites" that merges with the notion of programmable material. Through two different examples dealing with active acoustical impedance and elastodynamical interface, this paper presents used theoretical tools for designing specific applications of this new technology.

Motivation

Constant research for developing new materials better adapted for more efficient human applications, incorporating more and more new constraints such as the environmental damage (environmental impact, noise, recycling ...) led to study a new class of artificial multifunctional composite materials: the Metamaterials. These new materials presenting specific physical properties due to their micro or nano structuring, were originally developed to synthesize new electromagnetic permittivity indices or negative permeability. But in recent years, new research efforts have shown that the concepts could be transcribed in other areas of physics such as acoustics, mechanics or even robotics. Thus, the realization of new structured materials has led to obtain very interesting new physical features that can lead to the design of integrated multifunctional structures. In recent years, the technological revolution observed in the areas of Micro Electro Mechanical Systems can deeply extend the spectrum of future development of adaptive structures. One can now imagine full integration of hybrid systems consisting of adaptive materials, electronics, computing resources and power systems. The next generation of composite structures called "smart metacomposite" should take full advantage of these technological advances for optimizing their behavior1

The use of integrated and periodically distributed active systems of transduction could allow fine control of the material physical behavior. In this sense, we can speak of "integrated distributed adaptive metacomposites" conform to the notion of programmable material . This new technology should lead to new relevant applications for noise and/or vibration control, for achieving integrated surface actuators for adaptive applications.

2

Results

. This new approach represents a new challenge for creating intelligent hybrid materials.

This paper aims at showing specific applications of such new metacomposites for controlling mechanical and acoustical power flow into large space structure. In the first part, the concept of active acoustical skin is introduced and experimental validation is carried out (see Fig 1).

Perspectives

The studied adaptive metacomposite is totally apart from the existing technologies based on the use of non distributed and non integrated set of transducers. The main advantage stands on the capability of such system to guarantee robust efficiency of the systems but also the versatility and stability inherent to distributed control operators. From a technological point of view, size reduction of transducer's cell often goes together with cost reduction in production, increased sensitivity, and reduced energy consumption. Therefore, for these applications when dense distribution is targeted, MEMS appears as a technology of choice.

The addressed scientific and technological challenges also appear very attractive for aerospace applications where new lighter and functional materials are of great interest. Specific design of such metacomposites may allow synthesizing programmable materials with news functionalities as structural health monitoring and prognostic, shaping control or structural vibroacoustic specific properties in terms of transparency, absorption or emissivity.

Fig. 1 :

 1 Fig. 1: Metacomposite for realizing acoustical active skin. Left: Individual active acoustic cells and general view of the realized liner made of 4x12 cells and acoustical experimental set-up. Right: Transfer function between the input and output microphone,-active surfaces with control; • without control

Fig. 2 :

 2 Fig. 2: Metacomposite for realizing smart mechanical interface filtering vibroacoustic power flow. Left: Metacomposite made of piezocomposite cells and experimental FRF (free response in blue, controlled in green). Right: Energy distribution with absorbing and reflecting smart interface.

M Collet et al,

2009, Active acoustical impedance using distributed electrodynamical transducers, Journal of Acoustical Society of America, 125(2), 882 2 T. Toffoli, 1991, Programmable matter: concepts and realization". Physica D 47: 263