Conversion to Christianity in the Sasanian Empire

In the Sasanian empire, the relation to power of the different strands of Christianity (East-Syrian Dyophysite, West-Syrian Miaphysite, Chalcedonian) or Christian-oriented groups, partly derived from the landmark movements of deportation and missions starting in the East Roman lands, remained unsettled during the whole dynastic period (from the 3 rd to the 7 th century), moving from integration to defensive relation. Therefore the question of the conversion to Christianity is naturally correlated to the notion of identity affirmation on the one hand, within a minority context and an ethnic, cultural and religiously plural environment, 1 and to that of political loyalty towards the Persian king on the other, seeing that adhesion to Christianity within the Iranian territory challenged the very unity of the political body incarnated by the Sovereign. Periods of persecution of religious minorities, and specifically Christian minorities, between the 4 th century and the Arab period, led to a vast literary production that has fundamentally contributed to the shaping of identity in the Church of the East. Syriac sources present several types of accounts of conversion. The Acts of the Persian Martyrs often give priority to the conversion of great characters from the Mazdean society (from the 6 th century onwards especially); some hagiographies in fact mention cases of collective and widespread conversion (over a whole region for instance). In these accounts, the Sasanian king appears as the defender of Mazdaism, the official religion of the Empire, who intervenes on different levels in the process of conversion through a contrasting political approach, sometimes coercive, and sometimes supporting towards religious movements. These ambiguities lead to questions regarding the underlying interests behind such royal behaviour, but also in parallel concerning the writing process leading Christians to rewrite the persecuting king into a Christianised Sovereign. 2

THE KING, DEFENDER OF MAZDAISM

The notion of "State religion" cannot apply to Mazdaism (or Zoroastrianism), given the interpenetration of religion and politics with the very concept of Iranity in its ethnic and religious sense. [START_REF]L'Iran sous les Sassanides[END_REF] Philippe Gignoux and Gherardo Gnoli had well shown that Mazdaism is first and foremost an ethnic religion: 3 an Iranian subject professes Mazdaism, and if his parents are Mazdean, he becomes so through birth. LOYALTY AND DISLOYALTY, OR "HOW TO BE 'PERSIAN"?

There is a tight correlation between political loyalty and practiced religion. The Sasanian rulers explicitly affirm their belief in the Mazdean religion, even in a divine ancestry, and legitimate their power as descending from the god Ahura-Mazda: reliefs depicting scenes of investiture show the sovereign (who possesses xvarrah, "the radiance of glory") the same size as the divinities presenting him with the emblems of power. 4 In the Iranian empire, the notion of political loyalty towards the sovereign is at the heart of the problem of conversion: forfeiting one's forefathers' religion equated to renouncing the king's religion, but also led to a statutory transfer; the Iranian Christian converted from Mazdaism broke away from the world of ērān, and became a foreigner in his own country in a way. 5 The polarity between Ērān and Anērān -between the Iranian empire and its subjects on the one hand, and the non-Iranian world on the other -is a geo-strategic and politico-religious reality which explains, amongst others, in martyrological Syriac texts, the presence of recurring motives such as lese-majesty committed by Persian notability converted to Christianity. Abjuring Zoroastrianism in favour of another religion de facto led to social consequences, 6 and in particular forfeiture of any Sasanian administrative function, and sometimes even any privilege. The choice of a new name for those who converted -not always systematic, especially when the Middle-Persian family name remained significant from a Christian perspective -is also the public sign of such a renunciation, of a social break-away leading to conversion, as well as marking a change in allegiance, and the move towards a new and henceforth referring community. Names chosen are mostly Syriac -Syriac being the liturgical language of the Christians from the 4 th century onwards, among others -or even a mixed composition between Middle-Persian and Syriac. That is the case for Dād-Gušnasp, "given by Gušnasp", who chooses Dād-Īšō', "given by Jesus". 7 Nevertheless some rare examples enable us to qualify this pattern of exclusion of those converted to Christianity within the king's entourage. Indeed, high-ranking imperial officers occasionally kept their position some time after their conversion through royal consent, such as Grigor, Khurso the 1 st 's army commander-in-chief, or Yazd-bōzēd, a courtier of the Seleucia-Ctesiphon palace. This royal lenience was motivated by a rising awareness of the public use of such Christian notables in the service of a society they were perfectly integrated into.

This dual perception stemming from an opposition between Ērān and Anērān particularly applies to relations between Iranian subjects and their Byzantine neighbours. Conniving with the rival empire is one of the classic themes in East-Syriac literature reproached to the Christian community. 8 Since the promulgation of the Edict of Milan in 313 by Constantine, the position of Christians within Sasanian society had become somewhat ambivalent. But the possibility that such an edict might have a direct impact on the persecutions put in place by Šābuhr II over more than 40 years starting from 339, when Persia was battling out borders with Byzantium, is still being debated. In hagiographical literature, Christians are often accused by Persian authorities of complicity with an emperor deliberately qualified as their "co-religionist". 9 This perception is partly based on an extract from the Vita Constantini by Eusebius, who reports on a Letter sent by the Emperor to Šābūhr, a text translated early on into Syriac: its authenticity is not yet agreed on, even though it tends to be accepted, as the latest work by Kyle Smith seems to suggest. 10 According to Sebastian Brock, more than the Letter, it is Constantine's 7 The History of Mār Yazdīn, see Bedjan (1891: 564). 8 See Brock (1982). 9 For example, see in The Life of Simeon Bar Ṣabba'ē, Kmosko (ed.) (1907: 805-806). See Smith (2014). 10 Constantine's letter to Šābuhr II, of which Eusebius of Caesarea claims to give a Greek translation, emphazises the idea of a common destiny for Christians across the frontiers, under the authority of the Roman emperor who entrusts the protection of the Christian communities of Persia to the Mazdean king. Eusebius, De Vita Constantini, IV, 9-13. New status as universal patron of the Christians which was to contribute to an assimilation of these Persian communities to the Romans. In parallel, the hagiographical theme of the letter sent to the "Cesar" by the Christians of Persia in order to request his help spreads with a certain recurrence, since Persian epic literature still reproduced such a narrative (in particular the Šāhnāmeh by Ferdowsī in the 10 th century). 11 Christians subjected to the Persian king, friends of the enemy, and potential disruptive elements, become a leitmotiv in Mazdeo-Christian polemics, which deal with the concept of Christian loyalty / disloyalty to the king -an accusation which targeted converted Mazdeans in particular. 12 Such suspicions of unfaithfulness ran right into the 7 th century in Syriac sources, despite the situation of Christian communities in the East evolving in the wake of the Christological quarrels and the dogmatic definitions of the Councils, which rooted them in the Iranian territory once and for all: between 451 and 486, Miaphysite and East-Syrian Churches in Iran had broken away from the official religious position of Byzantine power, which supported the Chalcedonian cause. From the mid-5 th century onwards, converted Mazdeans had little choice other than political loyalty towards the king of kings. Therefore, the concept of heresiology remains at the core of the question of the political position of Christians in Iran (whether East-Syrian Dyophysites or West-Syrian Miaphysites) and of their relation to power and to the king himself.

On the other hand, we know of several Christian conversions to Mazdaism thanks to scarce information given by Syriac writers. Middle-Persian literature had not conserved any trace of these facts. In Syriac hagiographical narratives, examples, very scarce, are generally rather topical, no doubt because the communities these texts were destined to were depicted unfavourably. 13 These former Christians generally appear as careerists or opportunists, who adopt the official religion out of frustrated ambition. The civil authorities' reaction is approach and reinterpretation of the letter and its recipient in De Decker (1979). See also Raub (1997). Recently, Smith (2016: especially pp. 20-32); Frendo (2001). 11 In the Šāhnāmeh (or Book of Kings) of Ferdowsī, see Anōšagzād's letter to "Caesar," the Roman emperor, to gain support against his father Khusro I rst , Mohl (1877, repr. 1976: 180-181). See also Jullien, Ch. (2015). 12 See for example, in the context of the resumption of hostilities between Rome and Persia in 540, The History of Mār Abba, § 12, Jullien, F. (ed.) (2015: Syriac text pp. 14-15); French translation, ibid., pp. 15-17. When converting to Christian faith, former Zoroastrians have been accused of dual political loyalty by the Persians. 13 See Cantera (2010). not known; hagiographers underline that the power sought to deepen their new religious choice (considered as a renegade choice by their former co-religionists) by attributing administrative functions to them. Furthermore, some are described as the executioners of their former co-religionists' sentence: would that be a topos? or perhaps a test of the authenticity of their conversion?14 Hence, the writers of martyrological narratives gladly associate them with the apostle Judas.15 Some elements from the Acts of the Synods of the East-Syrian Church also mention defections. In 554 for instance, the first two canons feature the threat of adherence to Zoroastrianism of believers and clerics, disappointed not to have been considered by the ecclesiastic hierarchy, and seeking a better status amongst civil authorities. 16 IMPOSE AND RULE In a perspective where political loyalty and religion are intertwined, the imposition of Mazdaism was less the expression of a will to convert than a tool of power. One of the most relevant examples is no doubt the religious politics of Yazdgird II and his commander-in-chief (vuzurg framādār) Mihr-Narseh in the mid-5 th century Armenia. In these borderlands of the empire, an influenced zone shared between Persia and Byzantium, the Sasanian believed he was winning over then mainly Christian populations by demanding (especially of the notables) that they adopt Zoroastrianism. Such a political intention aimed at detaching Armenia from the Byzantine (Christian) sphere thanks to a forced religious rallying; it would lead on to the great revolt of the years 450-451 which caused the defeat of the Armenian troops during the Avarayr battle and important human casualties on the Persian side. Such circumstances are reported by historians Łazar P'arpec'i and Ełišē Vardapet. 17 Many priests pour faire détruire [une] église et attirer à eux une communauté qui ne dépendait pas d'eux, en exposant les prêtres, leurs confrères, aux chaînes, au pillage de leurs biens et à l'apostasie du christianisme", Chabot (ed.) (1902: Syriac text pp. 98-99; French translation pp. 355-357). 17 Garsoïan (2009: 69). Łazar P'arpec'i, History, Thomson (ed.) (1991: 34-36); Ełišē Vardapet, History of Vardan, Thomson (ed.) (1982: VI, 1-9). French translation Langlois (1867: 220-221, 296-297). Russell (1987). Garsoïan (1999: 125 n. 261, 20 n. 79).

were arrested and tortured according to the Pseudo-Sebēos, which also mentions deportations to the Khorassān region around 454. 18 But would it not be appropriate to look beyond the writings of Christian hagiographers, and see in this episode more than a political blunder committed by the Sasanian sovereign, and its dire consequences? The reality seems more complex, as is suggested by Nina Garsoïan, who refutes the theory of a deliberately malevolent political line conducted by the Sasanians towards their Armenian subjects. She has shown that Yazdgird II, after the Great Revolt, did not seek to amplify the de-Christianisation policy of the country. He finally allowed the notables to practice their faith. Furthermore, the main noble families had accepted the Persian suzerainty over their country rather well. 19 Yazdgird, vulnerable to military difficulties on the Northern front with the Hephtalite Huns, had to show some sort of leniency and agree to revise his project of forced imposition of Mazdaism over the Armenian territory.

It is also worth underlining along with Philippe Gignoux that proselytism in the Mazdean religion has not been proven for the Partho-Sasanian periods. Because of the notion of separation, judāgīh, a religious man could not have any relationships with non-Mazdeans or non-Iranians. 20 As such, the persecution of minorities does not per se imply forced conversion. Although Syriac martyrological literature mentions Magi forcing Christians to betray their faith in the king's name, these essentially concern former Zoroastrians to bring back; in other cases, the Mazdean clergy mainly sought to oppose certain customs deemed unacceptable -especially the burial of the dead, which was contrary to the Zoroastrian laws of purity. Rallying around the king's religion was thus perceived by the Mazdean authorities as contributing to bringing order into the world. 21 Examples of forced conversion must therefore be reinterpreted through the prism of context.

18 (Pseudo-)Sebēos, History, Thomson (ed.) (1999: 64-65). See also Daryaee (2012). 19 Garsoïan (2009: 72-74). Garsoïan (1998-2000: 314-318 and n. 39). See also McDonough (2006). 20 Gignoux (1997a: 17, 21-22). 21 On this subject, see Payne (2015: 30-33).

THE KING AND HIS CHRISTIAN SUBJECTS:

A CONTRASTED POLICY

The Sasanian Persians' policy vis-à-vis Christians was rather contrasted, wavering between open persecution (under Šāhbur II or Wahrām V's reign), and benevolent tolerance on other occasions (under Yazdgird I's or Khusro II's reign).

THE AMBIGUITIES OF ROYAL BEHAVIOUR

Royal interventionism

The king's direct interventionism at the high level of the Churches' hierarchy perhaps betrays a will to limit the movement of conversion to Zoroastrianism. In a recent thesis, Richard Payne has shown that Mazdean power could tolerate Christian expansion in exchange for compensation helping to maintain coexistence and distribution of space. 22 From the reign of Yazdgird I onwards, kings granted Christians the establishment of their own ecclesiastical jurisdiction. In return, bishops tacitly agreed to pay their allegiance to the sovereign, so as to maintain internal order and to cooperate with power. This theory of a modus operandi had already been looked into by Scott McDonough. 23 This tacit pact implied a ban on any opposition to the king's authority, and therefore also on any conversion within the aristocracy. According to him, the recurrent violent acts committed against the Christian minority do not reflect an intolerant coercive power, but rather a tacitly established socio-religious balance, which ecclesiastical elites had to respect for the sake of the churches' survival and for their interests. Thus, the king presided over the "improvement" -that is to say the validation -of the newly elected patriarch, and could even appoint him, as was the case on several occasions when he wished to reward his Christian physicians: the Catholicos Elisha, personal physician to Kawād I, who was invested against the Persian Church's candidate, provoking a thirteenyear schism in the first half of the 6 th century (from 524 to 537); Joseph (552-566), also physician to the court of Khusrō I, who was disowned by his clergy and deposed by the king after a series of complaints; or also Grigor of Kaškar (605-609), chosen by the sovereign Khusrō II in spite of protests of the East-Syrian bishops. 24 The profiles of patriarchs are known thanks to Syriac sources and correspond to types of social categories: well-read, learned, often physicians. Similarly, by refusing to grant investiture after the Catholicosal election, the royal authority asserted its power over its subjects and imposed its control over a religious minority both dependent and weakened. Between 609 and 628, the intervention of the Miaphysite Gabriel of Singar with Khusrō II led to a vacancy of the catholicosal chair for almost twenty years.

The influence of Christian queens on the king's religious policy

The influence of some royal wives sometimes contributed rather significantly to re-orienting the religious policy of the kings with regard to Christian religious minorities, and even to transforming their personal attitude. The historian Procopius mentions the Christian name of one of Khusro I's wives, Euphemia, a former deportee from Sura. Under her influence, the king proved to be more clement towards the elites of her home city, and even offered to liberate the prisoners he had sent into exile during the conquest. 25 In Khusro II's entourage was a Chalcedonian Christian, Maria, daughter of the Byzantine emperor Maurice, according to the Chronicle of Michael the Syrian. Another significant example of such an influence is queen Šīrīn, wife of Khusro II (590-628). According to the Byzantine historian Evagrius Scholasticus (536-590 -whose work was later picked up and amplified by Theophylact Simocatta at the beginning of the 7 th century), it was no doubt Šīrīn who encouraged Khusro II to offer ex-voto to the sanctuary of Saint Sergius in Reš'ayna (in Eastern Roman territory), in appreciation of the future birth of the heir to the throne. Furthermore the king attributed through the intercession of the saint the protection of the dynasty upon the coup of Wahram Čobin. The dedication was written not in Middle-Persian but in Greek, the language of the Byzantines:26 this royal gift was solemnly sent to the basilica through the [240]). Theophylact Simocatta, History V, 14, 8, Whitby -Whitby (eds.) (1986). On the reliability of the sources and historical problems in Theophylact Simocatta's work, see Peeters (1947: 5-56). According to Theophylact, Golindouš, who was a fervent follower of Saint Sergius, played an important role in the Queen's and Khusrō's personal life; they met her several times, probably at Circesium and Hierapolis, Peeters (1947: 25-26). Schilling (2008: 154-158).

patriarch Gregory of Antioch, with the approval of emperor Maurice. His open-mindedness towards the Miaphysite Christian community which Šīrīn belonged to is well known. Should this initiative necessarily be qualified as philo-Christian however? A priori, it resembles an approach reaching out to the virtus of a powerful protector. Such an initiative went on to raise the interest of the West, as is shown by the correspondence between bishop Domitian of Melitene and pope Gregory, while the conversion of the king AEthelbert of Kent was under way. 27 These ex-voto could also reveal a political attitude of the Mazdean sovereign towards Arab tribes who came to the sanctuary of Reš'ayna 28 and, in the case of the Lakhmids, precious auxiliaries of the Persians on the limes. Here, the assertion of such an act also has strategic repercussions, aiming to strengthen adhesion to a political koinon.

THE "PAGAN" KING, SUPPORTER OF RELIGIOUS MOVEMENTS

Religious communities sometimes managed to find in the supreme authority an ally and a support in favour of their expansion. Such a fact is well-known in the case of king Šābuhr I with Māni, who wrote in his honour the Šābuhragān, a kind of compendium of his doctrine around 240 (some Middle-Persian fragments of which have been found in Turfān). One of the acknowledged characteristics of this work, as Iris Colditz has shown, is the stylistic adaptation of its author to Zoroastrian terminology to present the theological elements of his religious system. 29 Such inclusive concern, which also pertains to a communication strategy, opened the possibility for dialogue with his Mazdean correspondent. Several Kephalaia mention the three audiences granted to Māni by the sovereign, enabling him to teach over the whole Persian empire. 30 Māni and his disciples were nevertheless made to revise their itinerary, no doubt due to the opposition of the Mazdean clergy; they travelled to Media 27 Peeters (1947: 44-45 n. 1). 28 On the devotion to Saint Sergius among the Arab tribes, see Fowden (1999: especially pp. 124-129.) 29 Colditz (2005). It seems that a part of the Šābuhragān was read by the Manichaean community during a liturgical office: Yoshida (2000: 91). See also Reck (2010). MacKenzie (1979: 500-534); MacKenzie (1980: 288-310). 30 Some regions of the Sasanian empire are mentioned: Fārs, Mayšān, Babylonia and Asūrestān. The first encounter took place around 240, Kephalaion I, 15, 31b-34; 16, 1-2; Kephalaion LXXVI, 184-186. Polotsky -Böhlig (eds.) (1940). Gardner (1995) Tardieu (1981), (1997 2 ). and to the regions bordering the Caspian Sea, as the Kephalaia and the Cologne Mani-Codex bear witness to. 31 Such a dichotomy between the interests of official authorities and the king's motivations are to be found in other contexts. One could also mention in that respect the taste of Kawād (488-496/498-531) for the theologico-politico Mazdakite movement, initiated in the 3 rd century by Zardušt, son of Xwarag, often called Mazdak the Elder, who advocated for a new social order by rejecting any form of private property. This perspective was justified by an eschatological legitimation and considered as a deviance from Mazdaism. Therefore Mazdak shook the very basis of Sasanian society, both nobiliary and religious, divided into classes, and questioned the government's functioning via Mazdean clergy and the notables. 32 Kawād wished to strengthen royal power and to undermine the power of feudal families and of the Magi. Despite once being influenced by these teachings (during his first reign), he referred back to them in order to impose territorial reforms serving his own interests. His eviction from the throne in 496 finally drove him to contend with the support of notability and clergy, and to renounce his personal religious inclinations in order to win back power. The choice of his son Khusro for an heir, instead of his elder, pro-Mazdakite son Kaūs, would pave the way for a violent repression of the movement.

Syriac writers thus put forward initiatives taken by Sasanian princes against the actions of the Magi: some of the sovereign's options might have jeopardised the cohesion of the empire (both Mazdean and Ērānian) and its unity.

It could be said that the search for Royal consent by the Church and religious movements was one of the conditions of their expansion. Within West-Syrian Christianity, 13 th century Syriac historian and compiler Grigor Bar 'Ebroyo relates how the missionary-bishop Simeon of Bēth-Aršam requested of king Kawād a free circulation permit through "the land of Sen'ar" (Babylonia) and Fārs. Such authorization depended on one condition: Simeon was expected to transmit to the king the names of the newly-converted. Indeed Bar 'Ebroyo underlines that bishop Simeon, wherever he went, obtained written commitments from the population, which he transmitted to the king, who 31 Römer (1994: 10-13). 32 Sources about the history of Mazdak and Mazdakism are not first-hand accounts and have a lot of contradictory data. See [START_REF] Christensen | Le règne du roi Kawādh et le communisme mazdakite[END_REF][START_REF] Christensen | [END_REF]Christensen ( , 1944 2 : 317-320) 2 : 317-320). Recently, Macuch (2015).

"confirmed them with royal seal". 33 The attribution of a circumscribed missionary territory, once the permit delivered, the validation sealed, in return guaranteed political authorities access to missionary activities.

THE "CONVERSION" OF THE KING On another note, and perhaps fuelled by such contradictions, Syriac authors sometimes surprisingly portrayed the persecuting sovereign in a very favourable light, even Christianising him, through hagiographic devices.

THE CHRISTIANISATION OF THE KING: A RHETORIC?

Syriac sources, and more specifically official texts from the Persian Church such as the acts of the East-Syrian synods, feature a rhetoric suited to sovereigns, who are not always favourable to the Christian cause. 34 Each report from a synodal assembly is preceded by a short eulogistic prologue, which reflects the allegiance of the Christian community to the master of the land, but perhaps also opportunism, since official documents provided by the ecclesiastical hierarchy were likely to be read by royal administration. Hence Khusro I was "the merciful and charitable king of kings" in the preamble of the 544 synod 35 -even though at this time, Christians were being imprisoned and the Catholicos himself was under house confinement. Occasionally, such phraseology went further than simple agreed-upon discourse. Such vocabulary could even go very far and echo expressions usually attributed to God alone: in 598, the Assembly of Sabrīšō' presented Khusro as "our adorable, victorious and merciful master," wishing him "long-living prosperity in all his enterprises," 36 he the "master for eternity". 37 The king was also a mediator, a "new 33 Bar 'Ebroyo, Ecclesiastical Chronicle, section II, Abbeloos -Lamy (eds.) (1877: 85-86).

On this practice, see Jullien, F. (2011, especially pp. 55-56); Jullien, F. (2016). 34 I allow myself to refer to Jullien, Ch. ( 2009) and ( 2011). 35 The Acts of the Synods of the East-Syrian Church, ed. CHABOT, J.-B., Synodicon orientale ou recueil de synodes nestoriens, Paris, 1902, Syriac text p. 70;French translation p. 320. 36 The Acts of the Synods of the East-Syrian Church, Chabot (ed.) (1902: Syriac text p. 207; French translation p. 470). 37 The Acts of the Synods of the East-Syrian Church, Chabot (1902: Syriac text p. 200; French translation p. 461). From a Pauline perspective, political authority could be seen as an image of the divine authority on earth, cf. Rm 13, 1-2: "Let everyone be subject to the governing authorities, for there is no authority except that which God has established. The authorities Cyrus ruling over all kings". 38 This indirectly suggested that political power could serve the East-Syrian cause.

THE CHRISTENING OF THE KING: A MESSIANIC IDEAL Some Syriac, Armenian or even Byzantine Greek sources have sought to Christianise the sovereign more explicitly by associating him with the community of believers. Following the assertions made by Procopius, the anonymous author of a Syriac chronicle from the 8 th century (Chronicon ad annum 724) curiously presents king Yazdgird I as "a Christian blessed among the kings". 39 Yazdgird's distancing himself from the Mazdean clergy and his attention to religious minorities 40 (two attitudes which earned him the nickname of "sinner" in later Arabo-Persian sources 41 ) probably explain his favourable depiction in the Syriac sources. The "Christian" king is by definition he who has been anointed, blessed. The hagiographical, but also apologetic writing, thus remodels the "pagan" king through a Messianic perspective able to rally the community behind the Supreme authority, even when he became the enemy and the persecutor -as was the case for Yazdgird in the last year of his reign. 42 that exist have been established by God. Consequently, whoever rebels against the authority is rebelling against what God has instituted, and those who do so will bring judgment on themselves". See The Chronicle of Seert, chapter LXXI, where such a position is justified, Scher (ed.) (1983: 502 [182]). 38 The Acts of the Synods of the East-Syrian Church, Chabot (ed.) (1902: Syriac text pp. 69-70; French translation p. 320). In a Muslim context, such a process of identification has been identified in narrative and epigraphic sources for the Mamluk Sultan Baybars for example, compared to Alexander the Great and to Moses, Eddé (2012). 39 Chronicon ad annum 724, Brooks (ed.) (1904: Syriac text p. 107); Latin translation Chabot (ed.) (1904: 137). Procopius, De Bello Persico I, 2, 8. On Yazdgird I's policy towards the Christian community in the Persian empire, and the mutual benefits each party received, see McDonough (2008b). After many years of persecution under the reign of Šābuhr II, the East-Syrian Church was strengthened and reorganized, and the Persian international and internal policy reinforced. 40 For the author of the pahlavi text entitled Šahrestānīhā-ī Ērānšahr, Yazdgird is said to have married the daughter of the reš galūtha, the Jewish Exilarch, whose name was Šōšān-duxt. See the extract, edited by Daryaee (2002: 20). Some scholars have questioned this assertion, as Herman (2012: 60-61). See Secunda (2013: 169 n. 46). 41 See Sauerbrei (1905) and McDonough (2008a). See also Mosig-Walburg (2009). 42 One may compare this conception with certain attitudes of Syriac authors to imperial power in the context of the Byzantine empire in Late Antiquity. Manolis Papoutsakis (2017) has

The most accomplished development in such a literary process is expressed in the sequences describing the christening of the dynast. In a noteworthy and richly documented study, Alexander Markus Schilling analysed the pattern for the 6 th and 7 th centuries amongst the different traditions of the Christians of the East. 43 Sebēos in Armenia or John of Nikiū in his Greek Universal Chronicle claim that Khusro I and his father Kawād professed the Christian faith in secreto and got christened. 44 Sebēos extensively details the Christian actions conducted by Kawād, who ordered that the liturgy be celebrated in his palace and that the Gospel be read in his presence. The Armenian historian goes as far as to say that upon his death, Christians buried him in the "sepulchre of the kings". 45 These presentations of pseudo-conversions also contribute to the Messiah-king theme, reflecting a communal hope and a political appeal.

The conversion of blood princes

These documents also mention tales of conversion to Christianity -and the subsequent martyrdom -of the children of royal blood. Several cycles can be mentioned when considering king Šāhbur II (309-379) who somewhat stood for the anti-Christian sovereign for generations to come, because of the 40year long persecution covering his reign. The best-known text is the Acts of Benham and his Sister Sara, probably written around the 5 th century -a novelistic passion, as has been shown by Bollandist Paul Devos. 46 Benham is curiously presented as the son of Sennacherib, king of Nineveh. During a hunting game, he met a hermit named Mattai, who converted him and cured the explored the theme of 'vicarious (Byzantine) kingship' in Syriac political theology through eschatological pattern and Biblical models. But as we can see, in the Sasanian milieu, the exegetical reconstruction was rather an image and a support for the rewriting history strategy. My thanks to the editors for this reference. 43 Schilling (2008). 44 John of Nikiū, Chronicle, Charles (ed.) (1916, repr. 1981: 154-155). See Schilling (2008: 185-189). Jullien, Ch. (2009). 45 (Pseudo-)Sebēos, History, chapter IX, Thomson (ed.) (1999: 9-10); French translation Macler (1904: chapter II). 46 Devos (1966). Syriac text edited by Bedjan (1891: 397-441). See Bruns (2008) and (2011).

For studies on the text, see Wiessner (1978). Younansardaroud (2002) and Holm (2014: 314-317).

young Sara who was a leper. 47 Both were baptised and had their throats slit by their own father who, following miraculous events, converted also. The very first lines mention a discreet reference to "Constantine, the victorious emperor," opposed to Julian the Apostate and Šāhbur II, the shamed emperors under whose reign the narration takes place. Such a reference motivates the narrative and reveals the author's intention to see Christian masters rule over the Sasanian empire as well as over the Eastern Roman empire.

A true narrative motive transpires through these writings, as other parallel examples show: the History of Aḥudemmeh, which reports the circumstances under which a child of royal descent was converted then christened, a son of Khusro I's, potential heir to the throne; 48 the Acts of Gubralaha and of his Sister Qāzō, 49 said to be the children of Šābuhr II, who both were converted and converted in turn. Nikephoros, the patriarch of Constantinople (806-815), preserves in his Breviarium (Ίστορία σύντομος) the narrative of one of the last sovereigns to govern the Sasanian empire, Šahrvaraz (for just a few months in 629). He was one of Khusro II's generals (spāhbed), to whom he was related through his wife. Nikephoros presents the pact concluded between Šahrvaraz and Heraclius: the former had to hand back the lands won over the Romans as well as the relics of the Passion of Christ, taken by Khusro II in 614, whereas the latter had to acknowledge and the usurper general, to support his illegitimate accession to the throne. He also welcomed his children into the Byzantine empire by associating them through marriage to the imperial family. 50 47 There are obvious biblical parallels, especially the healing of Miriam, the sister of Moses and Aaron, who was afflicted with leprosy, and whose skin had become white as snow, Nb XII, 10-15; cf. also Lc XVII,[11][12][13][14][15][16][17][18][19]Lc V,[12][13][14][15] Aḥudemmeh sent him at once to the Roman territory for security reasons. Nau (ed.) (1909: 33 [33]-34 [34]). 49 Gubralaha and his sister Qāzō are presented as the son and daughter of king Šābuhr II; they were converted under the influence of their Christian teacher, Dādōy, who also was put to death for his faith and became a martyr; formerly, Dādōy, member of the royal family, was a Magus. They were executed in 332. Syriac text edited by Bedjan (ed.) (1894: pp. 141-163; BHO 325). 50 Nikephoros of Constantinople, Breviarium VI, 8, Mango (ed.) (1990, § 17, p. 64): Heraclius gave the dignity of Patrice to Nicetas, son of Šahrvaraz, and gave his daughter Nike in marriage to Theodosius, the son he had with the empress Martina; he also gave his son Constantine [III] in marriage to Gregoria, the daughter of Nicetas. According to (Pseudo-)Sebēos, Šharvaraz decided to favor Christian communities as his intention was to conclude a close alliance with Heraclius; but the historian does not mention any conversion of his children to christianity. Heraclius only recognized in him and in his son the legitimate Cyril Mango in a study of the period has shown how this event had been prepared by the Byzantine chancellery and exploited by Heraclius, whose universalising ideology sought to impose over the Orient a policy close to the interests of the empire, whilst still maintaining the prospect of a conversion of Persia to Christianity. 51 For this reason, some scholars suppose that Šahrvaraz's two children might have become Christians. 52

Mirror-modelling

Several models seem paramount to these presentations: first the christening of Constantine, the image par excellence of the Christian king, who finds his theoretical support with Eusebius of Caesarea, whose historical work serves as a literary framework to many Syriac chroniclers (the Zuqnīn Chronicle, Chronicon ad annum 1234, the Chronicle of Michael the Syrian, etc.). 53 The figure of Constantine appears throughout the favourable descriptions of sovereigns in Christian historiography. 54 The conversion of the Lakhmid king No'mān III, christened by bishop Simeon of Ḥīra in 593, had a strong impact in Christian spheres. 55 It is also worth recalling that one of the key models behind these literary compositions stems from the New Testament tradition of Evangelical magi developed in the Opus Imperfectum in Matthaeum as well as in subsequent Syriac narratives (particularly the Zuqnīn Chronicle and the Revelation of the Magi), which tell, among other things, how the Magi upon arriving in Bethlehem from Persia to venerate the child Jesus were then heirs to the throne of Persia. (Pseudo-)Sebēos, History of Heraclius, Macler (ed.) (1904: chapter XXVIII). 51 Mango (1985: 117). Schilling (2008: 295-296). 52 Kaegi (2003: 188-206). 53 Concerning the diffusion and the Syriac translation of Eusebius of Caesarea's Church History, see Wright -McLean (1898). Duval (1907, repr. 1970: 188-191). About the importance and transmission of Eusebius's work in Syriac historiography, especially for the author of the Zuqnīn Chronicle, see Debié (2015: 297-300; 350-352). The apocryphal Acts of Sylvester, bishop of Rome, written in this city, may be known in the Syrian East since the VIth century as one of the metrical homilies ascribed to Jacob of Sarug mentions the theme. Frothingham (ed.) (1883: 167-242). 54 For the figure of the emperor Constantine as a literary theme in the East-Syrian hagiographical literature in the Persian empire, and the influence of his conversion, see Barnes (1985), Smith (2016), McDonough (2008a). See Lieu -Montserrat (1998). Conterno (2013; my thanks to Vittorio Berti for reminding me of this article). 55 See Jullien, F. (2009).

baptised by Thomas the Apostle who came to the Iranian land as a missionary. 56 In the Syriac tradition, the authors intentionally gave these characters the family names of Sasanian dynasts. In these descriptions of christenings, the Persian kings who adopt Christian faith are thus implicitly associated with these figures shown to be their forefathers.

These idealised presentations of the Messiah-king, loaded with political theology, have a very specific aim, which reflects identity issues. Different Christian communities from the Sasanian empire, rivalling over a missionary territory, and henceforth linked to the Persian land by their theological separation options, had little choice but to enter the political game to ensure their expansion, their permanence, their survival even. Whilst claiming their right to a deep insertion into the empire's society, administration and state apparatus, Christians developed narrative constructs as a prophylaxis meant to reassure, to create an idealised space within the empire, perhaps also to get even with an authority with ambivalent, almost persecuting motivations. Hagiographical writing thus becomes a formidable instrument to cast a favourable light onto a new political order in the Iranian world.

On this subject, seeJullien, F. (2012).

See the examples given byFiey (2004: 44-47, 54, 87, 111).

The Chronicle of Seert, Scher (ed.)(1911: 159 [67]). See The History of Mār Abba, § 25, Jullien, F. (ed.) (2015).

See The Acts of the Synods of the East-Syrian Church: "Ceux qui accuseront leurs voisins

[START_REF] Payne | A State of Mixture. Christians, Zoroastrians, and Iranian Political Culture in Late Antiquity[END_REF].

McDonough (2011: 303-305). See also[START_REF] Kalmin | Jewish Babylonia between Persia and Roman Palestine[END_REF];[START_REF] Widengren | The Status of the Jews in the Sasanian Empire[END_REF].

The Chronicle of Seert, Scher (ed.)(1919: 521 [201]-523 [203]).

Procopius, De Bello Persico II, 5, 28, Haury (ed.) (1963: 171-172).

Evagrius Scholasticus, Ecclesiastical History VI, Whitby (ed.)(2000: 312-316 [236]-

On these traditions, see Monneret de[START_REF] Monneret De Villard | Le leggende orientali sui Magi Evangelici[END_REF];[START_REF] Panaino | I Magi e la loro stella. Storia, scienza e teologia di un racconto evangelico[END_REF]. Ri (ed.)(1987); see[START_REF] Minov | Syriac Christian Identity in Late Sasanian Mesopotamia: The Cave of Treasures in Context[END_REF]) and (2017), and Schilling (2008: 159-185).


Petit Éric

Chêne Denis

Adaptive navigation in interactive systems: paradigm and solution A generic adaptive navigation method based upon Bayesian inferences and finite state machine

Keywords: Adaptive interfaces, personalization, navigation, predictive model, Bayesian inference

Adaptive navigation in interactive systems: paradigm and solution. A generic adaptive navigation method based upon Bayesian inferences and finite state machine

Eric Petit, Denis

INTRODUCTION

An adaptive interactive system is first and foremost a system in which the information provided by the user enables him to interact with it, as defined by Beaudouin-Lafon [START_REF] Beaudouin-Lafon | Ingénierie des systèmes interactifs[END_REF]. It is secondly, a system aiming to facilitate the achievement of the user task [START_REF] Norcio | Adaptive Human-Computer Interfaces NRL Report[END_REF].Therefore, an adaptive system has to be able to automatically modify its characteristics according to the user's needs [START_REF] Browne | The formal specification of adaptive user interfaces using Command Language Grammar[END_REF]. We propose an adaptive paradigm as well as a technical solution which considers the user's navigation in interactive systems. This paradigm is generic as it can adapt itself to all navigation tasks whatever are the devices enabling the navigation (mouse pointing, touch-based interface, vocal command) and whatever is the navigation hierarchy. This adaptive paradigm covers Oppermann's three steps [START_REF] Oppermann | Adaptively supported adaptability[END_REF]: the Afference, the Inference and the Efference. The navigation activities of the current user, as per Simonin and Carbonell [START_REF] Simonin | Interfaces adaptatives Adaptation dynamique à l'utilisateur courant[END_REF], are captured in real time (Afference step) and are directly used to generate a predictive model (Inference step) in charge of managing adaptivity (Efference step). Under this schema, each new interaction data refines the predictive model. The probabilistic inferences are based on the adaptive algorithm ABIT1 leveraging Bayesian theory. Our adaptive paradigm combines, in a flexible way and on a same continuum, adaptive guidance which facilitates to spot the most used paths during the navigation, adaptive shortcuts to reach more quickly the task's final state, and adaptive automatisms to increase efficiency without affecting effectiveness (to reach the right goal at the right time) nor satisfaction (the user's feeling of the interaction). These different modes of adaptivity "guidance, shortcuts and automatisms" are managed by the system during the interaction. This generic approach of adaptivity aims for the customization of the interaction. Such a dynamic adaptation of the interface to the current user's profile is consistent to Simonin and Carbonell's taxonomy [START_REF] Simonin | Interfaces adaptatives Adaptation dynamique à l'utilisateur courant[END_REF]. Within this scope, our user's activity model is focused on the user's navigation habits. A usual navigation task is then considered as a series of actions repeatedly carried out by the user on the interface. As a matter of fact, we do not deal with other aspects of the user's profile, such as preferences or abilities [START_REF] Martin-Hammond | Designing an Adaptive Web Navigation Interface for Users with Variable Pointing Performance[END_REF] which can be handled by other means especially by adaptable and flexible interfaces as proposed by the Design for All approach [START_REF] Stephanidis | User Interfaces for All: New Perspectives into Human-Computer Interaction[END_REF]. In this paper, we do not consider the interface adaptation to the environment or to the device, as developed by plasticity [START_REF] Thevenin | Plasticity of User Interfaces: Framework and Research Agenda[END_REF], as it could be dealt with separately.

The paradigm we are focusing on has to do with the adaptation to the user's behavior, modeled from his interaction activity captured by the interface. This approach is admitted in scientific literature as a likely way to improve the interface's usability, especially by reducing both the number of interactions and the complexity of the navigation the user has to deal with. It has been implemented by Horvitz [START_REF] Horvitz | Principles of mixed-initiative user interfaces[END_REF] in the LookOut project to support the user in managing his messages. It has also been experimented for a company management software [START_REF] Eichler | Adaptive User Interface Personalization in ERP Systems[END_REF] in order to facilitate form filling by highlighting the most used and important text fields [START_REF] Findlater | Ephemeral adaptation: the use of gradual onset to improve menu selection performance[END_REF]. In [START_REF] Soh | Deep Sequential Recommendation for Personalized Adaptive User Interfaces[END_REF] the prototype also highlights the interface most probable items based on the current user's activity with a deep learning machine, previously trained with other users. This study reveals limitations in terms of robustness due to the number of examples needed to train the learning model. And it suggests that a probabilistic approach would allow for a more reliable uncertainty measure, in agreement with the requirements of automatic adaptation. In [START_REF] Shilpi | Adaptive web navigation[END_REF] adaptivity focuses on a Web interface in which personalized links recommendations allow the user to get in one click from the home page to a favorite link embedded in depth, the link being automatically pulled up as a shortcut. A probabilistic approach like an improved Markov Chain model is used to predict links. To reduce its complexity, an offline learning step is however needed. Let's stress that most of these prototypes are specific to an application or to an applicative field.

In terms of cognition, beyond the general principles of cognitive ergonomics [START_REF] Nielsen | Usability engineering[END_REF], those expressed by Horvitz in his "mixed initiative" appear still relevant to us. They guided our design choices. These principles are:

• In many cases, systems can benefit by employing machinery for inferring and exploiting the uncertainty about a user's intentions and focus.

•

If uncertainty is too high, the system must be able to start a dialog with the user, but at the same time it has to consider the cognitive cost for the user.

•

In case of uncertainty, the system should provide efficient means by which users can directly invoke or terminate the automated services.

•

A weak prediction (under uncertainty) shall only be associated to an action with limited consequences. • Under uncertainty, prefer for "doing less with accuracy".

•

System must continue to learn from user's goals and needs through uninterrupted capture of his interactional activities and by automated reasoning within a Bayesian framework. Regarding the software engineering aspect, numerous architecture models have been proposed. An extensive synthesis is given in [START_REF] Akiki | Adaptive Model-Driven User Interface Development Systems[END_REF]. It results from this synthesis that designing adaptive interfaces must go through Model-Driven Engineering (MDE) allowing to apply adaptive behaviors to different levels of abstraction before deriving the final user interface that gets presented to the end-user. Moreover, this approach promotes a strong coupling between the user's actions and the system's answers, maintaining the user within the loop of Human Computer interaction. These "toolboxes" generally aim at two types of adaptation on the interface: the reduction of functionalities on display and the optimization of the items' spatial organization. So, they allow to encapsulate the complexity of these adaptive interfaces within reusable components, with an industrial ambition. Among these proposals, let's note the MyUI [START_REF] Peissner | MyUI: generating accessible user interfaces from multimodal design patterns[END_REF] development tool box which provides a general framework for the design and the automated generation of adaptive multimodal interfaces, in order to make them accessible, that is to say, able to adjust to the needs and abilities of each individual user. This software architecture relies, on one hand, on "design patterns" allowing to dynamically modify the interface at several levels: user profile, device profile, interaction modes and types of adaptation, and on the other hand, on a modelling of the applicative logic with a hierarchical finite state machine (type UML2 v2). A state chart diagram editor is provided in MyUI for easy coding. This model of abstract interface assumes that the dynamics of an interaction can be conceived as a succession of states, where each state represents a situation of interaction.

The evaluation of this framework for a Web TV interface has proved its technical feasibility. Unfortunately, its experimentation with elderly users encountered understanding difficulties regarding interface adaptation changes which were introduced by the system through a (too) rich dialog with the user. Indeed, in this prototype, too much dialog and explanation of the changes during the task resulted in high cognitive load for older users, therefore a failure. As advocated by Horvitz in his "mixed initiative", in such a situation, part of the adaptation should be automated. But in MyUI, as in most of development frameworks, adaptation criteria are managed by deterministic and immutable rules which do not allow a continuous evaluation of the costs-benefits ratio of the adaptations initiated by the system. In Horvitz approach, as in ours, the decision strategy relies on the ability of the system to infer probabilities on the user's intentions. Our solution focuses on the issue of adaptive navigation support in a hierarchical structured interface. It is also based on a finite state machine model, but unlike MyUI, our solution includes the probabilistic inference component along with uncertainty measures, as well as the decision-making mechanisms. The global model is described hereafter.

GLOBAL MODEL OF ADAPTIVE NAVIGATION

This new paradigm of interaction customization thus combines 3 modes of adaptivity: guidance, shortcuts, and automatisms. It is the result of a global approach considering multiple aspects: ergonomic (i.e. effectiveness, efficiency and satisfaction), applicative (navigation structure, interface items), mathematics (the probabilistic framework) and computer science (finite automaton). As far as ergonomics is concerned, the solution must convey greater effectiveness and efficiency which should be early detected and accepted by the user, especially as for the automatisms triggered by the system. Through this paradigm, we address the critical issue of the proper allocation of control between the user and the system, in accordance with predictability, intelligibility, stability, controllability, situation awareness and security requirements [START_REF] Bouzit | The PDA-LPA Design Space for User Interface Adaptation[END_REF]. As far as the system is concerned, it implies to design a sufficiently strong, flexible, and reactive modeling to propose relevant adaptations through a constant and close dialog between the system and the user. The reliable and real-time interpretation of the user's actions by the system is the cornerstone of this approach. This interpretation may either reinforce the adaptation towards a new habit, otherwise make a correction towards a former habit. To that end, we associate several adaptivity and software engineering techniques gathered in the general model called ABIT-SM 3 . We described them hereafter.

Logical navigation and execution model

This first component follows two goals: to provide a logical navigation model for all type of applications, and to produce an execution model that controls in real time the behavior of the interface in response to events generated by the user, as described in Figure 1. We chose a finite state machine (particularly Mealy's one) because this type of machine meets these two requirements while providing an appropriate framework to the Bayesian formalism that we are implementing. This type of finite automaton has been used for a long time in systems where complexity and reliability requirements are strong, for example in the field of aerospace. It implies a model-driven design of the interface.

A finite state machine is a so-called reactive system which performs an action in response to an external event (or input) given the interaction context held by the notion of state. This action (here the modification of the system) depends both on the current state and on the triggering event. Following this reaction of the system, a modification of the current state (or transition) occurs, the new state becoming the current state. This can result in the following mathematical formula:

[𝑠𝑡𝑎𝑡𝑒(𝑛 + 1), 𝑎𝑐𝑡𝑖𝑜𝑛(𝑛)] = 𝑓2𝑠𝑡𝑎𝑡𝑒(𝑛), 𝑖𝑛𝑝𝑢𝑡(𝑛)5 3 Adaptive Bayesian Inference Technique -State Machine Thus, a finite state machine consists of a finite state set (the whole interface possible states) and of a finite set of inputs (here the user's actions) that are mapped to the change actions within the interface. In this model, the machine can only be in one state at a time, the current state. The initial state determines the beginning of an interaction. Such a finite state machine is very well adapted to model a logical navigation hierarchy. It will be represented as a state-oriented graph. In this graph, each arc represents a transition, and a series of arcs represents a possible navigation path, the final state not being imposed. To illustrate our points, we will rely on the example of Figure 2. For example, if the interface is in the initial state 𝑠 : , then a user interaction defined by the 𝑎 :,; , 𝑎 ;,< , 𝑎 <,=: , 𝑎 =:,=> input series will lead to the state series: 𝑠 : → 𝑠 ; → 𝑠 < → 𝑠 =: → 𝑠 => . Each change of the current state corresponds to an evolution in the interface without the need to specify the exact nature of the modification. Such a graph characterizes without any ambiguity the full set of navigation constraints and therefore possible interface reactions. When a given path is regularly repeated by the user, it then becomes a navigation habit likely to produce dynamic adaptations. The detection of the user habits as well as their modeling are explained in the following section.

Bayesian predictive model

The detection of usage patterns is related to an issue of predicting navigation paths. These paths are based on past and present user activity. Considering the current path s(𝑛 -𝑘), … , 𝑠(𝑛 -2), 𝑠(𝑛 -1), 𝑠(𝑛) where s(𝒏) represents the current state and 𝑠(𝑛 -1), 𝑠(𝑛 -2), … , 𝑠(𝑛 -𝑘) represent past states, then the prediction consists in determining the entry leading to the next most probable state s(𝑛 + 1). However, the crucial point is the uncertainty measure associated with this prediction. Indeed, our paradigm is based on getting a reliable measure of uncertainty, at each step of the navigation, in order to dynamically find the best adaptability strategy.

Here, the uncertainty is potentially present both at the output and at the input of each current state. For example, this is the case with the state 𝑠 E , because the latter has 2 incoming paths and 3 outgoing paths (the exits). The rigorous solving of such a problem appeals on Bayesian theory, which makes it possible to formalize a mode of rational reasoning in the presence of uncertainty. In this context, Bayesian inference allows a degree of probability to be associated with each outcome of the current state.

The Bayesian selected network is the naive one. It is based on the acceptable assumption of conditional independence of the predictive variables knowing the common causal hypothesis: S(𝑛 + 1). It is shown in Figure 3 below. The random variable S(𝑛 + 1) has a finite number of values corresponding to the possible outcomes from the state S(𝑛). The random variable S(𝑛 -1) then represents the possible states immediately connected to the input of the current state S(𝑛). The S(𝑛 -2) variable concerns the states of rank 𝑛 -2, and, so on as illustrated in Figure 4. So, the first level antecedent states are grouped together to form the variable S(𝑛 -1). Those of the previous level are grouped together to form the variable S(𝑛 -1). The output states are grouped together to form the variable to be explained: S(𝑛 + 1).

Thus, at each step n of the navigation path, Bayesian inference provides the a posteriori probability of state n + 1: During interaction, this probability is updated for each activated state of the automaton. Therefore, each state has its own Bayesian network that is updated locally and independently, thus limiting the number of calculations. In this schema, the strong coupling between the finite state machine and Bayesian inference (distributed in the states graph) provides the predictive navigation model able to supporting adaptive mechanisms. Note that the implemented inference algorithm (ABIT) operates in an adaptive and supervised way, taking into account the recency of activity data. Indeed, the calculated belief degree must simultaneously reflects the frequencies of occurrence of the taken paths but also their recency in order to give more importance to the last actions of the user. That implies the progressive forgetting of the past. These properties endow our algorithm with both learning and unlearning capabilities.

P(s(n + 1) / s(n), s(n -1), s(n -2), … )
Armed with this predictive model, we can design and operationalize the complete paradigm comprising the 3 adaptive modes: guidance, shortcuts and automatisms.

Adaptive guidance

This first assistance mode intends to guide the user through his navigation by highlighting the interface commands items (inputs) associated to the most used paths. Therefore, each state of the current path independently manages the guidance applicable to its possible entries now considered issues. For example, 𝑠 E state can highlight the 𝑎 E,J , 𝑎 E,K and 𝑎 E,=: issues. The highlight of one or several issues in the user interface can be concretely done by any means revealing the preferred way out. However, these means are not handled in this paper as it concerns the final user interface. The mechanism for activating local guidance is based on crossing the 20% probability threshold. This low threshold enables to quickly consider a budding habit. Moreover, it allows the possible activation of several guides when exiting the current state, as illustrated by a screenshot of our interactive demonstrator in Figure 5.

On the figure, the initial state of the interaction (𝑠 : in this example) is represented with a dark green button. The current state, here 𝑠 E , has a black border. The adaptive guidance part is marked with a thick red line covering the arcs of the graph. It is worth noting that the 𝑠 E state leads to two guides towards the 𝑠 J and 𝑠 K states. This type of guidance is known as a continuous guidance as it crosses several hierarchical levels. It is a local guidance if the habit is only for a portion of the navigation path. If several paths are competing at a given state, for example 𝑠 E → 𝑠 J facing 𝑠 E → 𝑠 K → 𝑠 =; , then learning one leads to unlearning the other following the Bayesian approach, the guidance adjusting accordingly. The guidance is incentive and not much intrusive but yet has to be responsive. That's why its trigger point is associated to a 20% probability. Thus, it is proposing by indicating the most used paths during previous interactions. In doing so, it can quickly include the changings in the user's habits. In return, this may be inappropriate but without having any consequences as it is just an "inducement to go". Above all when it is appropriate, it highly simplifies the spotting of the right path (cognitive saving) and even more, if it is associated to a selection operation on a control, it turns the required interaction to a simple validation action (motor saving).

Beyond the cognitive and motor savings, the adaptive guidance has low impact on the interface as for structure or additional items, which is not the case with shortcuts.

Adaptive shortcuts

This second assistance mode deals with an automatic generation of shortcuts. It aims at enabling the user to reach in a more efficient way the final state of his navigation task. These are macro-commands produced by the interface according to the design choices of the application. For example, the created shortcuts could be presented on the home page, in a dedicated area, or even in other places on the interface according to its functional and hierarchical structure. The principle is to generate these shortcuts on the basis of the adaptive guidance mode, provided there is a continuum. More precisely, a shortcut will be created on the usual path marked with at least 3 successive guidance towards current state. It will be created by the current state located at the end of the guidance series but registered on the starting state of the path. In the previous example, if the user validates the 𝑎 E,K input, the 𝑠 K state will become the new current state. The continuum conditions being fulfilled, a shortcut should be created and available in state 𝑠 : , as illustrated in the screenshot of Figure 6. This shortcut corresponds to the series of inputs that can be used to go from state 𝑠 : to the final state 𝑠 K (marked with a yellow star) by only one command (the macro 𝑎 :,; , 𝑎 ;,E , 𝑎 E,K ). In this example, two actions are therefore saved for the user. Now if the usual path is extended through to 𝑠 =; state, then a new shortcut will automatically be generated (macro 𝑎 :,; , 𝑎 ;,E , 𝑎 E,K , 𝑎 K,=; ). This shortcut will then replace the previous one because it is considered as more efficient. Let's point that first shortcut will be immediately recreated if the user follows the same path without exceeding state 𝑠 K , then considered as final, thus implementing the principle of reversibility. This general mechanism enables to manage several shortcuts attached to a same state (initial or not) according to a FIFO 4 list principle: the last updated shortcut goes up the list and the older ones disappear.

Note that the adaptive shortcuts, either presented on a list or in a dedicated area, are additional items. Hence, they overload the interface resulting in higher perceptual processing cost. They are certainly useful as they accelerate the execution (motor saving) and make the commands go up to the current state level in order to be seen (cognitive saving). Indeed, without the adaptive shortcuts, the usual commands would be buried deep in the hierarchy. Their structural impact goes beyond the current state overload. By levelling the functions, they can contribute to deconstruct the mental representation of the organization of the interface that the user has been able to build (loss of representation). To justify their use as an adaptive component, the motor gain has to be superior to the negative characteristics as a whole. That's why we have conditioned their creation on the implementation of at least 3 successive guides on the current navigation. They are thus more rarely set up and more efficient on a motor point of view, the navigation jumps being larger. Let's now consider the alternative approach of automated macro-commands.

Adaptive automatisms

This third assistance mode is related to adaptive automatisms. Like the guidance, it is locally activated (at the current state level) and concerns the downstream portion between the latter and one of the following states.

The idea is that the navigation runs autonomously on part of a usual path, without user action. However, this adaptivity mode is only triggered when a strong habit is detected, that is to say, a path prediction associated to a high level of confidence. It can be applied to one or several portions, might they be adjacent or not. Indeed, the flexibility of the mechanism authorizes to automate only a part of the predicted path where the uncertainty is very low. This mode is also based on the probability of the current prediction, but here considering a high threshold of 80%. By using the demonstrator's previous learning, we can for example create a strong habit by repeating the following series: s : → 𝑠 ; → 𝑠 E → 𝑠 K → 𝑠 =; . Then, after 8 repetitions (to get an idea), automatisms arise, as illustrated in Figure7. They are represented by a right-oriented black arch. In all cases, an activation of the first entry by the user (here 𝑎 :,; ) will be necessary to trigger the whole chain of automatisms up to the final state, here 𝑠 =; . Indeed, we defined the following rule: an automatism cannot begin without a prior action by the user in order to secure the handling. On a cognitive point of view, it is important to point out that before the standalone mode of execution happens, the user will have had a reflective perception of his usage habits thanks to the adaptive guidance, or even shortcuts. He will thus be prepared to understand this automatic assistance which he will be able to link to his routine behavior. It should be specified that if an automated path covering 3 or more portions does exist, then the equivalent shortcut also exists. The user can thus choose the most convenient way to accomplish his task. Finally, note that the automatic mode can occasionally occur during an interaction in order to facilitate one or two successive transitions where a shortcut should be of little interest. It thus can be said that the 3 modes are in fact complementary, each of them bringing its own assistance suited to a user's habit. On the other hand, a temporal order exists. The guidance is first implemented bringing markers (like affordances) to the user, thereby reducing its cognitive load, and facilitating his appropriation. Then come the shortcuts (which can be accessed from different areas of the interface) as soon as the habits are settled, offering powerful macro-commands. As for the automatisms, they only appear if the user has performed marked routine behaviors which implies he has gained ability in the use of his interface. These automatisms reveal themselves on non-ambiguous portions matching with frequent used paths. They can arise at the beginning, the middle or the end of a task according to the user's habits and according to the navigation structural model as well as the uncertainty measures. A "middle" or "final" automatism might then be interpreted as a little boost from the system during interaction.

Reversibility of the adaptations

This adaptivity paradigm cannot be considered viable without any adaptation reversibility mechanisms in order to ensure a good user control on the system. This includes the possibility to correct an action and to change habits. That's why a specific "undo" command has been thought and integrated in the solution's global architecture. On one hand it enables the user to undo an action pushed by the system (especially several chain automatisms), or even an action done by him, and on the other hand it enables the system to unlearn a former habit and at the same time learn a new one. To illustrate these different aspects, let's consider the habit case: s : → 𝑠 ; → 𝑠 E → 𝑠 K → 𝑠 =; , just after its standalone execution. The use of the "undo" command will cancel the action performed by the system and therefore will bring the current state back to 𝑠 ; , this by a retrograde course of the path. All the potential automatisms are temporarily disengaged, the system giving back the control to the user. Then the user can make another navigation choice, as for example follow the 𝑠 ; → 𝑠 E → 𝑠 J 𝑝ath, ending in 𝑠 J state. If this choice is due to the circumstances, then the nature of the adaptivity will remain unchanged. But if the choice is due to the development of a new habit, then the predictive model will evolve consequently. More precisely, the 𝑠 E node becoming a possible turning point and opening on two likely issues: 𝑠 J and 𝑠 K , its Bayesian network will be modified. Actually, this competition between the two issues has an immediate effect: it creates uncertainty on 𝑠 E node which leads to a strong probability decrease associated to 𝑠 K , resulting in the rapid cancellation of the local automatism. It is worth repeating that for this mode the activation threshold is quite high, which boosts a quick unlearning in case of uncertainty. In the present case, the 𝑠 E → 𝑠 K automatism will be undone but the other automatisms: the upstream one (𝑠 ; → 𝑠 E ) and the downstream one (𝑠 K → 𝑠 =; ), will remain active because non-affected by the change of behavior. This stresses the flexibility of the adaptivity paradigm driven by probabilities and closely linked to the user's actions.

DEMONSTRATION

This adaptivity paradigm has been designed in conjunction with its algorithmic and software development, leading to ABIT-SM framework. The latter gives a generic implementation of the solution in the Kotlin language suited to multi-platform mobile development. On this basis we have developed a mobile application running on a touch-based tablet. Thus, it makes it possible to test the various concepts previously described in an interactive way for a sufficiently rich and universal navigation where the hierarchical structure could be more general than a tree (e.g. a lattice structure). To demonstrate the generic nature of our approach, we have chosen to design an interactive system not depending on an applicative field. Therefore, the application exposes an abstract interface. It represents the application structure as a state transition diagram. Thus, it reveals the underlying execution model of the final user interface (not yet defined). For this demonstration, we have selected a usage scenario combining the three adaptivity modes as well as the use of the "undo" command. We start from the automated learning of the path: s : → 𝑠 ; → 𝑠 E → 𝑠 K → 𝑠 =; and begin to create a new habit corresponding to the sequence: s : → 𝑠 ; → 𝑠 E → 𝑠 J . The user has been subjected to a now inappropriate automatism and found himself directly thrown from 𝑠 ; to 𝑠 =; .

First, the effect of the "undo" command cancelling the automatic executions (left-oriented black arches) and enabling the user to regain control is illustrated on Figure 8. So, the system goes back up to s2.

Finally, we create a third habit related to the task: s : → 𝑠 ; → 𝑠 < → 𝑠 == , keeping the two other habits. As the user goes automatically to 𝑠 E from 𝑠 ; state, the use of the "undo" command is required to go back to 𝑠 ; and then chose the 𝑎 ;,< input giving access to the new path. Repeating this operation undoes the middle automatism because of the competing paths and the resulting uncertainty. By force of habit, the guidance appears on the 𝑠 ; → 𝑠 < → 𝑠 == portion together with a third shortcut allowing access to state 𝑠 == . With the confirming habit, an ending task automatism appears on portion 𝑠 < → 𝑠 == , as illustrated on Figure 10. As uncertainty appears at state 𝑠 E , the automatism 𝑠 E → 𝑠 K is canceled. After a few repetitions of the new path, an alternative guidance shows up at 𝑠 E and a second shortcut is created, available at 𝑠 : , as illustrated in Figure 9. The 𝑠 ; → 𝑠 E automatism is still active (black arch) as well as the one on portion: 𝑠 K → 𝑠 =; . To sum up, we have continuous guidance for the two usual paths, two available shortcuts and two automatisms: one at the middle of the task and one at the end.

DISCUSSION AND CONCLUSION

We have presented a new paradigm for the dynamic adaptation of an interface to the user's navigation habits.

This paradigm makes it possible to assist the user in his current task of navigation through a flexible and dynamic combination of 3 modes of adaptivity. This combination adjusts the nature of the automated assistance according to the degree of uncertainty on the navigation paths predictions. The latter is calculated at every step and for each activated state of the interface. Therefore, inside a very interaction, several modes can be invoked in different places of the interface and at different times of the ongoing task. The automatic mode whose benefit is potentially significant for the user but with an expensive cost if an error occurs, will only be invoked in case of a high confidence level. Moreover, while navigating, its application will have a variable impact, more or less local according to the uncertainty measure along the path. The guidance mode, in case of a prediction error has less consequences and should be invoked with greater tolerance considering a low probability threshold. Nevertheless, the activation of this mode will always be linked to the user's usage, thus respecting the predictability criterion. Furthermore, this guidance being not locally exclusive, it could lead to several navigation incentives, thereby lessening the risk of error. Last, the shortcut mode, generated along with the guidance mode, leads to macro-commands, the user being free to use them or not. This generic paradigm also includes the critical command "undo" assuring the user the control of his interface, especially in case of behavior changes, might they be circumstantial or lasting ones, or simply due to an error. We noticed that the effect of this command depends on the nature of the previous actions. Its use gives the system a means to detect a possible change of habit, therefore improving its learning accordingly. In this paradigm, no need for an explicit dialog, the system only needs to implicitly interpret the user's current actions on the interface. Let's keep in mind that having to begin a dialog with the user to clarify his intentions can be quite costly on a cognitive point of view. The alternative may be to "do less" but correctly or, as Horvitz puts it, to "gracefully degrade" the accuracy of the automated service. So, it appears that a key point of the adaptive interfaces is to adjust permanently the nature of the adaptations according to the quality of the predictions given by the system, which involves a rigorous processing of uncertainty.

At the technical level, we have demonstrated the feasibility of a generic and robust solution in the form of a general prediction and adaptation model, underpinned by a finite state machine which defines the abstract interface. This systemic model is both a user and task model as well as an execution and adaptation model. Our ABIT-SM architecture embeds a large part of the implementation complexity of the paradigm opening up for an industrial manufacture. We particularly aim at everyday life applications that integrate complex navigation.

In this paper, we gave numerous elements of description and justification, both practical and theoretical, supporting the validity of our proposal. The latter has been materialized by an interactive prototype exposing an abstract interface, non-specific to a particular application, in order to remain generic. Our future work will consist in determining an appropriate application framework to test these concepts through an experimentation.

Figure 1 :

 1 Figure 1: navigation and execution automaton

Figure 2 :

 2 Figure 2: state-oriented graph of a user interface In this oriented graph, 𝑠 7 represents the interface state of index 𝑖. The user's actions (inputs) are associated to the arcs and represented by 𝑎 7,8 , 𝑖 and 𝑗 being the indexes of the starting states 𝑠 7 and ending states 𝑠 8 of the transition. The interface evolution is driven by the inputs 𝑎 7,8 which are also the entries of the automaton.

Figure 3 :

 3 Figure 3: Naive Bayesian network

Figure 4 :

 4 Figure 4: Formation of the discrete random variables from the current state.

Figure 5 :

 5 Figure 5: guidance's activation while on current path, including 2 guides from the state 𝒔 𝟓 .

Figure 6 :

 6 Figure 6: automatic creation of a shortcut in 𝐬 𝟎 to reach 𝒔 𝟗 .

Figure 7 :

 7 Figure 7: Implementation of 3 automatisms on the current path from state 𝒔 𝟐 .

Figure 8 :

 8 Figure 8: effect of the 'undo' command, here cancelling the last 3 actions initiated by the system.

Figure 9 :Figure 10 :

 910 Figure 9: activation of a new guidance from 𝒔 𝟓 (towards 𝒔 𝟖 ) with simultaneous creation of a shortcut

Adaptive Bayesian Inference Technique IDDN1 .FR2 .0013 .2300214 .0005 .S6 .P7 .20208 .0009 .20700

Unified Modelling language

ACKNOWLEDGMENTS

Many thanks to Hélène Joucla, Valérie Ledunois and Aymeric De Solages, for their welcoming and relevant contribution.


R Blin
email: blin@ehess.fr

Does partial pretranslation can improve low ressourced-languages pairs?

We study the effects of a local and punctual pretranslation of the source corpus on the performance of a Transformer translation model. The pretranslations are performed at the morphological (morpheme translation), lexical (word translation) and morphosyntactic (numeral groups and dates) levels. We focus on small and medium-sized training corpora (50K ∼ 2.5M bisegments) and on a linguistically distant language pair (Japanese and French). We find that this type of pretranslation does not lead to significant progress. We describe the motivations of the approach, the specific difficulties of Japanese-French translation. We discuss the possible reasons for the observed underperformance.

Introduction

There are many techniques to improve the performance of a neural translation system without changing the size of the training corpus, without increasing the computational power, and independently of the tuning of the translation system: enriching vocabulary embedding (e.g. [START_REF] Ding | How do source-side monolingual word embeddings impact neural machine translation[END_REF]), injecting linguistic information (e.g. [START_REF] Sennrich | Linguistic input features improve neural machine translation[END_REF]), reordering (e.g. [START_REF] Kawara | Preordering encoding on transformer for translation[END_REF]), etc. These techniques are absolutely crucial for language pairs with few corpora, and when computing power is limited.

We propose here to apply another technique, which to our knowledge has not been studied so far with neural translation. It consists in pretranslating short segments of the source corpus. We proceed with handmade rules and vocabulary translation lists. We will observe its effects on Japanese-French, with several corpus sizes (50K-2.5M bisegments). This is indeed a language pair that remains poorly endowed with large, freely accessible and good quality corpora.

The aim of pretranslation is to reduce the linguistic distance between the two languages and to facilitate learning. The advantage is that it can be applied even with limited knowledge about the translation rules between the two languages. In addition, building the pretranslation rule by hand does not necessitate annotated resources (that maybe do not exist).

In section 2 we present the difficulties specific to French-Japanese. In section 3 we describe the type of pretranslations we have carried out. In section 3, we describe an experimental setup used to evaluate the effects of those pretranslations. We will see in section 5 that it is difficult to correlate these results with the properties of the corpora.

Challenges of Japanese-French Translation

Japanese and French are known to be linguistically distant languages. We present here briefly the most notable points of divergence, which may impact their joint treatment. Japanese and French use different writing systems. Japanese uses about 2300 characters. French uses about 50 (including capitals). The two systems share only Arabic numerals and some English words written in Latin characters in Japanese texts. The sharing of vocabulary is therefore of little interest when training a translation model.

Word formation in the two languages does not correspond. French is a richly inflected language. Flexion concerns almost all parts of speech. On the contrary, Japanese morphology varies only for a part of verbs and adjectives (native Japanese lexical stratum). Japanese is also considered an agglutinative language. With the same meaning, many expressions in Japanese and French are not formed at the same level: expressions formed at the morphological level in Japanese are formed at the syntactic level in French and vice versa (see example below "seem not to want to drink"; CONJ:conjugation suffix):

no-mita-kuna-katta-rou Word order is different at several levels. In writing, Japanese is an SOV language where the order is semi-free, with possible pragmatic effects. French is a SVO language. Word order also diverges within phrases. In Japanese, in most cases, the complements (nominal, propositional) precede the head of the phrase. In French, they appear on either side of the head:

daidokoro 1 no 2 ookii 3 teeburu 4 kitchen GEN large table grande 3 table 4 de 2 <la> cuisine 1 "large table of <the> kitchen"
A major source of difficulty in comparing or translating the two languages is the absence in Japanese of many components that are obligatory in French. Japanese uses few quantification marks (determiners etc.) and makes extensive use of bare nouns. A bare noun phrase will often have several possible translations in French (see also a discussion involving Japanese and English in [START_REF] Bond | Determiners and Number in English contrasted with Japanese, as exemplified in Machine Translation[END_REF]. Many sentence components are elided in Japanese. Japanese is a pro-drop language. Unlike in French, the place of absent components is not occupied by a pronoun. In addition, titles and press headlines have a specific syntax in Japanese [START_REF] Noguchi | midashi" no 'bunpo' -kaidoku heno tebiki to shomondai-['Syntax' of the "headlines" -Problems and guidance to the reading[END_REF].

Constraints between distant structures exist in both languages but do not concern the same parts of speech. In French, distant words can share the same gender and number marks. This is the case of subject-verb agreement, for example. Japanese is known to use floating quantifiers consisting of a numeral and a classifier. The choice of the classifier depends on the quantified noun.

[kami/pen] 1 wo kitto san-[mai/bon] 1 kau. {paper/pen} O cert. 3 -CL/CL 1 buy (He) certainly buy three papers/pens.

Pretranslation applied here

We study 5 levels of pretranslation. The pretranslations are applied recursively (the pretranslation of corpus i is added to that of corpus i -1). The idea is that a single modification cannot substantially improve the translation. We must therefore study an accumulation of pretranslations. An example of sentence pretranslation is given in the table 8. C0 is the baseline corpus.

C1: Compositional structures

We pretranslate two structures whose translation is in general independent of the context: numerals and dates. Japanese numerals come in two forms: Sino-Japanese system (百万) or anglophone "Arabic" system (1,000,000). The treatment of numerals may seem anecdotal, but we found that they were unexpectedly poorly translated by the models trained on small corpora. This can be explained, among other things, by the variants of notation. Pretranslation is therefore both a translation and a kind of normalisation:

The translation of dates requires a triple processing: reordering, pretranslation of the numerals, global translation.

1910年 year 3月 month 3日 day reorder → 3日 day 3月 month 1910年 year transl.
→ 3 mars 1910 Ambiguous expressions are left as they are, such as 一日 which means «un jour» or «le premier (du mois)».

Choosing not to translate ambiguous expressions has disadvantages. Indeed, it is possible that some occurrences of an expression are not translated. We are not able to assess the number of cases involved, nor the effect on the performance of the translation model.

C2: Suffixes, punctuation, proper names

Affixes are translated if their translation is "relatively" regular: 主義 (shugi) → isme. In general, the linguistic segmentation of Japanese separates the suffix from the radical. But in order to get closer to the French form, which does not separate the suffix from its radical, we do not separate in Japanese either. It is left to the statistical segmentation (BPE) to separate or not. The form is systematically put in the singular.

共産 N 主義 SUFF («kyōsan shugi») → 共産 isme → 共産isme
Punctuation is simplified and brought closer to that of French. This concerns mainly interrogative marks: か? → ?; か。 → ? .

Most of the changes in C1 concern the translation of proper names. We used several resources: an existing dictionary (jalexgram 0.37), Wikipedia translations and translations available in unidic-cwj. Considering the possible segmentation errors and translation errors (in particular from the Wikipedia), we roughly filtered: the ratio <source word length / target word length> must not exceed 0.4 (in bytes). We do not translate one character-words because they are frequently ambiguous. We obtain a dictionary of 30,000 translated proper names.

It should be noted that the transcription (e.g. Hepburn: Tōkyō, Kunrei: Toukyou, other: Tokyo) is not unified within the corpora and within the dictionary. It is therefore possible that a translation in the dictionary does not correspond to a translation in the target corpus.

C3: Common nouns (CN)

In French, CNs are variable in number and are associated with a determiner, which does not exist in Japanese. We pretranslate using the singular and do not add a determiner. Most CNs have several translations, which depend on the context. For all occurrences of a noun, we will use a single translation, and always the same one. This is therefore a very rough pretranslation. 36,700 CNs have been translated (from Jalexgram).

C4:Verbal nouns (VN) in nominal position

Japanese VNs (e.g. benkyō) have two distributions. Followed by a support verb, they behave as verbal radicals (e.g. benkyō vn suru "litt. study do; to study"). Otherwise, they are used as CNs (e.g. "studies"). The corresponding forms in French occur with a determinant, but mostly at the singular form. We translate VNs in nominal position, in singular, without determiner. Here again, this is a rough pretranslation. 7,350 VNs were used.

Experiment

Corpus

We use the Cjafr-v3 (Blin and Cromières, 2022) corpus1 . To our knowledge, this is the largest and freely available "ready to use" corpus currently available. The core contains 400K bisegments translated by humans. A majority of the bisegments are from TED [START_REF] Reimers | Making monolingual sentence embeddings multilingual using knowledge distillation[END_REF]. We add a part of the extension of Cjafr (≈2M of bisegments). It is made of various crawled corpora.

From this corpus of 2.5M bisegments, and after preprocessing, two training corpora of 50K and 500K bisegments are randomly extracted. For all experiments, the fine-tuning and evaluation corpora always remain the same (but the preprocessing is different).

The evaluation is carried out on two test corpora: PUD (1000 bisegments)2 and ted.test (3000 bisegments from TED corpus).

The corpus are morphologically analysed and segmented using mecab [START_REF] Kudo | Mecab: yet another part-of-speech and morphological analyzer[END_REF] and the Unidic-cwj [START_REF] Oka | Unidic for morphological analysis with reduced model size by review of crf feature templates[END_REF] dictionary. Some segmentation errors are corrected with ad-hoc rules (the same for all the experiments, including the baseline corpus). We apply thus a BPE segmentation (12K words for Japanese, 8K words for French; with SentencePiece [START_REF] Kudo | Sentencepiece: A simple and language independent subword tokenizer and detokenizer for neural text processing[END_REF]). The segmentation model is trained with the pretranslated train corpus. A description of the corpora is provided in Tables 3, 6 and7).In particular, we evaluate the proximity (with BLEU) between the pretranslated corpora and the target corpus, after BPE segmentation.

Training and results

The training is executed with Opennmt-py.2.0.0 [START_REF] Klein | OpenNMT: Open-Source Toolkit for Neural Machine Translation[END_REF] 3 . the batch_size is set to 2048 and the word_vec_size is set to 256.

In order to reduce the variance of the results due to the random nature of the training, we perform three trainings for each corpus and calculate the average. Table 1 and 2 provide the BLEU scores4 . For the evaluation, punctuation is separated. The raw scores are of course very different depending on the size of the training corpus. To compare them, we propose the proportional difference between the baseline score (A) and the score after pretranslation (B): B-A/A.

Several additional settings have been experimented but no one provided a significant difference with those described above. For the sake of place, we do not present them here. Those settings are: segmentation with shared vocabulary (BPE segmentation set to 16K words; evaluation with TER [START_REF] Snover | A study of translation edit rate with targeted human annotation[END_REF]

Discussion

As expected, pretranslation increases the proximity (measured in BLEU, on BPE segmented corpus) between the Japanese and French corpora (see Tab.5). For the smaller training corpora (50K bisegments), the progression is a little less than 1 point (knowing that in percentage, this represents 50%). The PUD corpus shows the most notable progress (+1.63 points). However, it should be noted that, whatever the corpus, the proximity is low, with or without pretranslation (<3.80 BLEU).

The results do not show significant progress. In some cases, there is even a deterioration. Nor is there a clear causal link between the (quantified) characteristics of the corpus and the results.

Compared to the size of the training corpus (50K, 500K or 2.5M bisegments), we observe a systematic but modest improvement for the 500K bisegment corpus. This behaviour is correlated with a very slight superiority of the vocabulary variety (tab.4). In other words, for this size of corpus and type of corpus, the greater variety of the corpus could improve the translation.

Concerning the test corpora, we observe better results for PUD. Again, in parallel, we note that the variety of vocabulary is slightly higher for PUD (tab.4). Moreover, if we observe the proportional difference of the number of words in Japanese and French (# words ja -# words fr/ # words ja) we see that PUD is close to train.2M5 (tab.7). We also observe a (very slightly) higher proximity between ja and fr (BLEU) for PUD (Tab.5).

We also repeated the C2 and C4 experiment with vocabulary sharing (word number for BPE segmentation is set at 16K). The results are slightly lower than with the separated vocabularies. This can be explained by the low number of common word strings, even after pre-translation. Vocabulary sharing does not improve the results after pre-translation.

It is difficult to establish a causal relationship between the (quantifiable) characteristics of the corpora and the results. Indeed, it can be observed that corpus features such as proximity (BLEU) or vocabulary variety are present in the base corpus CO. The pre-translation does not change anything, and even reduces these features.

Conclusion

Based on the assumption that proximity between languages could facilitate learning by a neural translation model, we locally pre-translated words and morphosyntactic structures in the source language. No significant results were observed. Some results have deteriorated. We tried to correlate these results with quantifiable features of the corpora but no clear causal relationships appeared. Several hypotheses are possible. Either the pre-translation is not thorough enough and more components need to be pre-translated to see a notable positive effect. In this case, a more massive intervention should be considered, or even coordinated with an intervention on the target. Or the linguistic characteristics of the two languages do not allow any progress through pre-translation. This could be confirmed by carrying out the same work on another language, for example SOV language (e.g. Basque) and/or with a poorer morphology SVO language (English). We have observed three corpus sizes. There is a slight improvement for the corpus of 500K words (vs 50K and 2.5M).

Table 2 :

 2 BLEU score; corpus ted.test; proportional variation with respect to the baseline

  To better understand the reasons for this behaviour, we propose to repeat the experiments with intermediate corpus sizes .

	train.2M5	val	PUD ted.test
	C0 2,527,216 2,964 1,000 2,929

Table 3

 3

				: # bisegments
		train.50 train.500 train.2M5	val	PUD ted.test
	fr	30.44	31.33	30.88	21.24 27.49 24.93
	C0	31.74	32.27	30.80	18.81 25.83 24.95
	C1	31.11	32.48	31.01	19.20 25.93 25.07
	C2	32.30	32.48	30.95	19.34 26.54 25.37
	C3	31.42	32.13	31.14	20.25 26.90 25.06
	C4	31.78	32.25	31.03	20.21 27.19 26.13

Table 4 :

 4 Vocabulary variety (# of original words in a sample of 10K words/10K).

		train.50 train.500 train.2M5 val PUD ted.test
	C0	2.84	2.60	2.17	0.07 0.49	0.12
	C1	2.82	2.60	2.18	0.12 0.70	0.18
	C2	3.13	2.87	2.46	0.42 1.43	0.44
	C3	3.61	3.40	2.92	0.64 1.95	0.67
	C4	3.79	3.57	3.07	0.65 2.12	0.74

Table 5 :

 5 Proximity of the ja src corpora and the fr corpus; BLEU scores

		train.2M5	val	PUD ted.test
	C0	19.36	25.12 33.10 25.91
	C1	19.32	25.08 33.00 25.93
	C2	19.37	25.13 33.40 25.96
	C3	20.04	25.93 34.51 26.84
	C4	20.19	26.09 34.84 27.00

Table 6 :

 6 Average length of the japanese segments, after BPE segmentation

		train.2M5	val	PUD	ted.test
		48,970,553 71,855 33,673 79,270
	C0	-0.11%	3.61% -1.70% -4.27%
	C1	-0.28%	3.47% -1.99% -4.20%
	C2	-0.05%	3.66% -0.82% -4.08%
	C3	3.43%	6.94% 2.49% -0.84%
	C4	4.19%	7.61% 3.45% -0.24%

Table 7 :

 7 # words; proportional variation with respect to the French target corpus

Download fromhttp://crlao.ehess.fr/ rblin/ tajafr.php

Test corpus used at CoNL 2017 shared task on parsing Universal Dependencies. lindat.mff.cuni.cz/ repository/ xmlui/ handle/11234/1-2184

The hyperparameters are those suggested in opennmt.net/OpenNMT-py/FAQ.html#how-do-i -use-the-transformer-model; 2021/06/01

Calculated using multi-BLEU www.statmt.org/wmt06/shared-task/ multi-bleu.perl, default settings

Acknowledgements

I sincerely thank Fabien Cromières for his valuable advice and comments.


Maria Laura Mayol

Pierre-Antoine Joulin

N K Dimitrov

A Lovera

S Eldevik

Alexis Cousin

Martin Guiton

Uncertainty evaluation of BEM approaches for offshore wind turbine design

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

Uncertainty evaluation of BEM approaches

for offshore wind turbine design

• Aerodynamic methods

• Different levels of complexity

• Blade Element Momentum (BEM):

• Widely used for design • Steady conditions, empirical corrections • Low computational cost • Limitations for large/floating wind turbines

• Vortex method: • Reducing vortex sheet:

• Shed Merging:

• Shed filaments are progressively merged

• Tip Vortex:

• Filaments are conserved in the near wake. Then, a transition to "Tip Vortex" is applied • Teesside:

• South Brittany: ➢ relative discrepancy between the BEM and Vortex GPs Conclusions Summary, Conclusions and future work

• Comparison between BEM and Vortex models for two different offshore technologies:

• BEM models, using different ASHE tools (Diego, Hawc2, and DLW)

• Vortex model, Castor + DLW

• Several GP models have been trained based on results from both the BEM and Vortex simulations.

• Benchmark, overall good agreement between BEM codes.

• BEM vs Vortex differences are higher for the floating wind turbine.

• GPs or metamodels can be used in two different ways:

• either to select a conservative response with a specified confidence level for all relevant input scenarios • or to fully quantify the uncertainties between both approaches.

Future work

• Estimate the model uncertainty by comparing engineering models with high fidelity LES simulations.

  DTU, EDF, IFPEN): • HAWC2 / DIEGO / DeepLines Wind TM (DLW) • Coupled with servo-hydro-elastic models • Vortex Method (IFPEN) • CASTOR + DLW • Coupled with servo-hydro-elastic models have been trained based on different relevant responses in the simulation results from both the BEM and Vortex simulations. • Output: metamodels for BEM and Vortex • For several variables and inputs parameters • Integrated forces on the rotor (Thrust, Power, Torque) • Aerodynamic forces along the blades (over 5 points)

IFP Energies nouvelles, Rueil-Malmaison, France.

Denmark Technical University, DTU, Lyngby, Denmark

EDF R&D, EDF Lab. Saclay, France

DNV Group Research and Development, Høvik, Norway

IFP Energies nouvelles, Solaize, France 1

Main objective: reduce the Levelized Cost Of Energy (LCOE) by reducing the uncertainty in the complete chain of modeling OWTs in a wind farm

Main goal: to evaluate the uncertainty of Blade Element momentum approaches, by comparing them with a high fidelity model

Acknowledgements

This project has received funding from the European Union's Horizon 2020 Research and Innovation Programme under Grant Agreement No. 101006689


Nicolas Bonfils

Guillaume Huwart

Martin Guiton

Timothée Perdrizet

Wake Parametrization and surrogate modelling for loads prediction

come