851-860.

Western music, be it instruments, concerts or theory, has influenced Chinese music or musical life only since the 1910s. During the first centuries of contact, there was mutual interest and curiosity, but even more an awareness of the differences between the respective systems. In contradistinction to the policy held by Jesuits in South America, especially in Paraguay, Jesuits in China did not attempt to mix the two cultures. Yet, their missionary strategy did not exclude Western music, which if accepted by people at the court might positively influence the Emperor himself towards other Western achievements

Western instruments and music

Not long after their arrival in 1583, the missionaries founded a church in Zhaoqing 肇慶, and Western instruments caused great sensation [START_REF] Fr I | [END_REF] . There were organs and keyboard strings instruments in Macao as early as 1601. 2 Matteo Ricci (Li Madou 利瑪竇, 1552-1610) brought musical instruments as gift to the Wanli 萬直 emperor twice, first on his arrival in Beijing in 1598, but without success, then on his return to Beijing in 1601. These instruments featured a string instrument called by Ricci gravicembolo 3 or manicordio 4 Schall von Bell also wrote a lesson for keyboard instrument in Chinese accompanied by a few psalm melodies. 9 The historian Tan Qian 談 遷 , who visited Schall in 1654, saw an instrument (tianqin 天琴) with 45 strings and 45 keys. [START_REF] Qian | Johann Adam Schall in the Pei-yu lu of T'an Ch'ien and in the Eyes of his Contemporaries[END_REF] Since some Chinese sources describe an instrument with 72 strings, [START_REF][END_REF] which were struck, 12 it is clear that several keyboard strings instruments had been brought, mostly harpsichords.

Among European instruments which were brought to China, keyboard strings instruments aroused substantial interest. The Kangxi 康熙 emperor himself is said to have played a Chinese tune on an instrument with 120 metal strings 13 , and that some of his own sons as well as eunuchs were taught to play it. In 1671, Kangxi asked Ferdinand Verbiest (Nan Huairen 南懷仁 1623-1688, arrived in 1659) to teach him music; the latter had Tomé Pereira (Xu Risheng 徐日升 1645-1708, arrived in 1673) come especially for it from Macao.

The first description of an organ, an instrument previously unknown, is found in Giulio Aleni's (Ai Rulüe 艾儒略) Zhifang wai ji 職方外紀 (1623), which reports on the organ in the cathedral of Toledo (Spain) [START_REF] Aleni | Tianxue chuhan 天學初函[END_REF] . Pereira built an organ for the Nantang 南堂 church at Beijing as well as a set of bells which chimed automatically 15 . Wu Changyun 長元 in his Chenyuan shilüe 宸垣識略 (1788) gives a desription of this organ. [START_REF] Yi | [END_REF] Not a few missionaries were good instrumentalists, and had brought Western instruments with them which they played at the court. The most eminent musician among them was Teodorico Pedrini CM (De Lige 德 理 格 1671-1746), an Italian who, being exceptionally gifted and well-trained in music, was therefore sent by Propaganda Fide to China to please Kangxi. After his arrival in Beijing (February 1711), he endured a difficult life as a courtier who served three emperors, was imprisoned, but succeeded in building two new organs and teaching some of Kangxi's sons. Under the pseudonym of Nepridi, he left a manuscript with a set of twelve Italian-style sonatas, entitled Sonate a Violino Solo col Basso del Nepridi, Opera Terza and preserved in the Beitang Library. They were possibly influenced by Arcangelo Corelli (1653-1713) who was active in Rome when Pedrini was studying there. [START_REF] Pé | 12 sonates de Pedrini pour le violon seul avec basse continue[END_REF] Apart from this sonatas, very few Western scores are documented as having been brought to China. [START_REF] Verhaeren | [END_REF] An exception was a famous opera by Niccolo Piccinni (1728-1800), La

Cecchina, played at the imperial court soon after its (Italian) premiere in 1760. It pleased the Qianlong emperor so much that he had a stage built and established a troupe to play it again and again. [START_REF] Ginguené | Notice sur la vie et les ouvrages de Niccolo Piccinni[END_REF]

Western theory of music

On the level of Western theory of music, the most important introduction was Lülü zuanyao 律呂纂要 (Compilation of Musical Theory) written by Tomé Pereira on behalf of the Kangxi emperor, and completed after Pereira's death by Pedrini. [START_REF] Ms | discovered in the Beiping tushuguan by Wu Xiangxiang 相湘, who first published his discovery in Guangzhou da guangbao 廣州大光報[END_REF] The work was revised and partly integrated as the last part of Lülü zhengyi xubian 律呂正義續編, the supplement to the imperial encyclopedia on music Lülü zhengyi 律呂正義 (part of Lülü yuanyuan 淵源, 1723). [START_REF]Also included in Siku quanshu 四庫全書; there is a German translation[END_REF] It features a presentation of the tonal system, rhythmic and staff notation, and is a good example of the difficluties involved in translating musical terminology from a European into a Chinese tradition.

Liturgical music

Another interesting testimony for the blending of Chinese and Western music certainly is litrugical music. The first record of a Mass accompanied by is the Christmas celebration in Beijing in 1604. 22 Organ (or régale) [START_REF]Possibly this "organ" was in fact a "régale[END_REF]

On Chinese music

The early reports on Chinese music to Europe are scarce and not very positive.

On March 3rd, 1599 or March 16, 1600, Ricci heard a Confucian ceremony with music in Nanking [START_REF] Fr Ii | n. 5. Not "catholic mass[END_REF] Ricci also made comments on Taoist music, where he found great disconsonantia. 30 In the eighteenth century, the two main sources that introduced Chinese theory of music, music and scores into Europe, mainly France, are letters 31 published in 1735 and an unpublished from 1754 by Joseph Marie Amiot. [START_REF] Picard | It was recently identified[END_REF] The latter had been previously and mistakenly looked upon for during years as a supposed translation of Li Guangdi 李光地 Gu Yuejing zhuan 古樂經傳 (1708) [1727], while it was in fact an original work. These were followed in 1776-1779 by other important writings by Amiot who also sent Chinese instruments and scores. [START_REF] Cf | Une grande collection: Mémoires concernant les Chinois (1776-1814)[END_REF] Amiot compiled a series of Chinese musical scores in gongchepu 工尺譜 notation, also translated into some kind of staff notation, which present suites (Divertissements) that were played at the court and whose style is related to the tradition of Shifan 十番. 34

Musicology and history of musical exchanges

Numerous records, mostly from the Western side, relate how Jesuits played Western music and the reaction of Chinese listeners. The Jesuits also played Chinese music on their own instruments, and it is said that some Chinese, including Kangxi himself, 35

  PICARD, François, "Music (17th and 18th centuries)", in Prof. N. Standaert (ed.), The Handbook of Oriental Studies, Christianity in China (vol. 1), Leiden, E.J. Brill, 2001, pp.

  and, in Chinese, among other names, "Western string instrument" xiqin 西琴. It is not yet quite clear what kind of string instrument this manicordio was; it appears to have been most probably a clavichord 5 . On behalf of the Wanli emperor, four eunuchs learned to play the instrument Ricci had given. Diego Pantoja (Pang Diwo 迪我 c. 1571-1618, in Macao in 1597) was asked to teach them music at the Palace, but after one month of study, they could hardly play one piece 6 . Ricci wrote eight songs for the harpsichord Xiqin quyi ι濡ム文, now lost except for the texts, of moral more than of Christian content 7 . Adam Schall von Bell (Tang Ruowang 湯若望 1591-1666, arrived in 1630) was latter ordered to repair the instrument (o cravo) given by Ricci and to translate the Latin psalm-verse written on it. 8

  and other instruments were played in Sciala (Shanlan 後痼) at Ricci's funerals on 22 April 1611.24 On this occasions, however, one may have played merely Western music and instruments. The first indications for Chinese dramatising moments in the Old Testament, and were to be sung on traditional Chinese tunes, mostly in yiqiang 弋腔 style.25 Joseph Marie Amiot (Qian Deming 錢德明, Toulon 1718 -Beijing 1793, in Beijing since 1751) compiled a collection of sacred music Shengyue jing pu 聖樂經譜 containing

	thirteen liturgical songs in Chinese. In 1779, he sent this collection to "monsieur Bignon,
	bibliothécaire du Roi". 26 Most of these songs are prayers allready translated during the late
	Ming (attributed to Niccolò Longobardo 龍華民 1565-1655) and found in the official prayer-
	books (Shengjiao rike 聖教日課). The title of these prayers are: (1) Prayer at the Aspersion
	with Holy Water, (2) Prayer at the beginning of a service, (3) Our Father, (4) Hail Mary, (5)
	Salve Regina, (6) Sanctissima, (7) Prayer for the Holy Sacrament, (8) Act of Humility, (9) Prayer
	at the Elevation of the Host, (10) Prayer at the Elevation of the Chalice, (11) Prayer at
	Communion, (12) Prayer to Jesus Christ, (13) Prayer at the End of a service. 27 The music,

liturgical music date of a century later. In 1710, Wu Li SJ 觱 Yushan 漁山 (1632-1718), a famous painter and poet, wrote his Tianyue zhengyin pu 天樂正 in Mary, others recounting or even purely Chinese, and in a style related to Nan Bei qu 南北曲, was written by Chinese, among them Manchu Ma André (died in 1768), a member of the Congregation of Musicians at the Beitang (Northern Church) in Beijing. The absence of a Kyrie or Gloria in Chinese is due to the fact that during the 1750s and 1770s Propaganda Fide had forbade the singing in Chinese of parts of the Mass such as the Kyrie, Gloria, etc., proposed by missionaries in Beijing and Sichuan. Only prayers which did not belong to the liturgy of the Mass itself could be sung in Chinese by those who attended Mass but not by the priest and his assistants. 28

  played Chinese music on Western instruments. No record exists, however, of Westerners having played Chinese instruments.The first book in Chinese about Western music was published as early as 1713, while the first Western study of Chinese music was written in 1754. Both included musical scores, theory, history, explanation of the respective musical systems, and both were written by Christian missionaries, respectively Pereira and Amiot. But the first study in a Western language about musical exchanges between China and the West, by Tchen, was not published until 1974, while its Chinese counterpart, by Tao, only dates from 1994. Zhifang wai ji 職方外紀, 1623, in Mohai jinhu 墨海金壺 and in LI Zhizao 李之藻 (ed.), Tianxue chuhan 天學初函, 1626, repr. Taibei, Taiwan xuesheng, 1965. [AMIOT, Joseph Marie], De la Musique moderne des Chinois, ms., Beijing, 1754. Paris, Bibliothèque nationale de France, Rés. Vmb. ms. 14. AMIOT, Joseph Marie (Qian Deming 錢德明), "Divertissements chinois", "Musique sacrée. Recueil des principales prières mises en musique chinoise Shengyue jing pu 聖樂 經譜", ms., 1779, Paris, BNF Bréquigny 14. [AMIOT, Joseph Marie], Mélanges sur la Chine et les Chinois, ms., Beijing, 1779, BNF Bréquigny 121-122. AMIOT, Joseph Marie, Mémoire de la Musique des Chinois tant anciens que modernes. Paris, Nyon l'Ainé, 1779, fac simile . Fredric LIEBERMAN (ed.) & Bryna LIEBERMAN (trad.), Dissertation on the Music of the Chinese, Ancient and Modern. By Jean-Joseph-Marie Amiot, Genève, Minkoff, 1973. D'ELIA, Pasquale, Fonti Ricciane, Storia dell'introduzione del Cristianesimo in Cina, 1942-1949. DU HALDE, Jean-Baptiste, Description géographique, historique, chronologique, politique, et physique de l'Empire de la Chine et de la Tartarie chinoise, Paris, P.G. Le Mercier, 1735. FENG Shike 馮時可, Pengchuang xu lu 篷窗續 , Hangzhou, c. 1620, in TAO Ting 鳥⒁, (ed.), Shuofu xu 郛續, 1657. GAO Shiqi 高士奇, Pengshan mi ji 蓬山密記, in MIAO Quansun 繆匨孫 (1844-1919), (ed.), Guxue huikan 古學彙刊, Shanghai, Guocui xuebao she, 1912. MARECHAL, (ed.), Lettres édifiantes et curieuses, écrites des missions étrangères, par quelques Missionnaires de la Compagnie de Jésus. 32 vol., Paris, various printers, 1729-1774. [PEDRINI, Teodorico], Sonate a Violino Solo col Basso del Nepridi Opera Terza, undated ms. (78 pp.), Beijing tushuguan. PEREIRA, Tomé (XU Risheng 徐日升), and Pedrini, Teodorico (De Lige 德理格), Lülü zhengyi xubian 律呂正義續編, 1713, compiled and revised by order of Kangxi emperor. Translation: see Gerlinde Gild-Bohne (1991). [PEREIRA, Tomé (XU Risheng 徐日升)], Lülü zuanyao 律呂纂要, ms, Beijing tushuguan. RICCI Matthieu, TRIGAULT, Nicolas, Histoire de l'expédition chrétienne au royaume de la Chine 1582-1610, Georges BESSIERE, (ed.), Paris, Desclée de Brouwer / Bellarmin, 1978. RICCI, Matteo (LI Madou 利瑪竇), Xiqin qu yi 西琴曲意, in LI Zhizao (ed.), Tianxue chuhan 天學初函, 1626, repr. Taibei, Taiwan xuesheng, 1965, pp. 283-290. SCHALL VON BELL, Johann Adam, Historica Relatio de Ortu et Progressu fidei orthodoxae in Regno Chinensi, 2nd ed. Ratisbonne (Regensburg), 1672, repr. 1942. TACCHI VENTURI, Pietro, Opere Storiche del P. Matteo Ricci, Macerata, F. Giorgetti, 1911-1913. TAN Qian 談遷, Beiyu lu 北游碌, 1653-1656, Beijing Library, repr. Shonghua Shuju, 1960 (repr. 1981). TRIGAULT, Nicola, Christiana Expeditione Apud Sinica, Auciore (Augsburg), 1615.

	Primary sources
	ALENI, Giulio (Ai Rulüe 艾儒略),


est destinée au dépôt

Evolution of the follicular in vitro to maturation-inducing hormones at the end of vitellogenosis in rainbow trout Salmo gairdnerii : Role of estradiol-17β

Bernard Jalabert, Alexis Fostier

To cite this version:

Bernard Jalabert, Alexis Fostier. Evolution of the follicular in vitro to maturation-inducing hormones at the end of vitellogenosis in rainbow trout Salmo gairdnerii : Role of estradiol-17β. International Symposium on Salmonid Reproduction, Oct 1983, Bellevue, Washington, United States. hal-02783542


Isabelle Charleux

On Worshipped Ancestors and Pious Donors: Some Notes on Mongol Imperial and Royal Portraits 1

In this paper I would like to present some of the choices made by the Mongols in the uses and representations of their sovereigns' portraits in both sculpture and painting.

By taking examples of preserved portraits or those known about through textual descriptions, from the Mongol Empire to the Ch'ing dynasty, I will try to understand why the portraits were made and their symbolic role in state ideology compared to other material representations of power. The dramatic destruction of the Mongol artistic heritage means that it is almost impossible to draw up a chronological account from a reliable corpus. The history of Mongol art can only be reconstituted on the basis of a few scattered works.

STATUES OF GREAT MONGOL ANCESTORS

The Mongols worshipped anthropomorphic portrait statues of their former rulers. The oldest known representations of the Mongol emperors were lifelike portrait statues of Chinggis Khan, written about 20 years after his death by two 13th-century travellers: Benedict the Pole, who encountered Batu on the Volga in 1246, 2 and John of Plano Carpini, who visited Güyük's court in Central Mongolia in 1245. 3 The statue described by Plano Carpini was gilded or made of gold -the colour of power in the nomadic world -and stood on a cart in front of the imperial tent where it was worshipped every day as their "god."

1) -the archaeologists believe that Yang-ch'ün-miao could be the main sacrificial site of the Yüan dynasty, where the emperors sacrificed to the Sky and to their ancestors.

The Mongol stone men are believed to represent dead noble Mongols but their ethnic identity is still under discussion -they could have been erected by the Önggüd, the Qonggirad, or by the Yüan nobility. 10 Fig. 1. One of the marble statues wearing a dragon robe at Yang-ch'ün-miao, Cheng-lan banner, Inner Mongolia, Yüan dynasty. Kai Shan-lin, 1997, 347.

FEEDING THE ANCESTORS, FEEDING THE ONGON 翁袞 翁袞 翁袞 翁袞

These statues were worshipped during sacrificial rituals and were fed with meat and milky products. The statue of Chinggis Khan mentioned by Plano Carpini received offerings of food. The Yüan dynasty stone statues generally hold a cup, like the Turkic statues, and it is believed that the cup would contain food or an alcoholic offering. They were also given offerings such as coins, cattle bones, and sapeques found in small pits by the statues' side. According to a Yüan dynasty poem, a statue that might be one of the Yang-ch'ün-miao effigies had wine poured in its mouth and its body coated with fat, while a horse was cut up in front of the statue as the sacrificial meat, and an officiant sang and beat time with his feet. This poem recounted the sacrifice made by the powerful imperial (ch'üan-ch'en ch'in-ch'ai-jen 權臣欽差人) legate Temür 鐵木爾 from Yen 燕 (Ho-pei 河 北 province) to the marble statue of a deceased Great Preceptor (hsian-t'ai-shih 先太師), 70 li 里 northwest of Luan-tu 灤都 (i.e., Shang-tu). 11 These statues were fed like ongon so that the ancestor could receive the sacrifice. Small bronze ongon dating from the Mongol Empire hold a cup in their hand (Fig. 2) like the life-size stone statues. Ongon are zoomorphic or anthropomorphic supports made of various materials (such as felt, wood, metal etc.) to feed the spirits. 12 Human spirits that 10 Bayar, op. cit., 2002. 11 Hsü Yu-jen 許有壬, "P'ei Yu-t'ai-fu T'ai-p'ing-wang Chi-hsian-t'ai-shih Shih-hsiang 陪右太夫太平 王祭先太師石像," in Chih-cheng-chi 至正集 (Taipei: Hsin-wen-feng, 1985), chüan 卷 6. could dwell in an ongon were either angry and potentially dangerous human spirits, or great ancestors. The Mongols used to feed their ongon by smearing their mouth and sometimes the whole face with fat and cooked meat, by sprinkling and fumigation. In exchange, the spirit would protect the household or clan, bestow prosperity, and ensure success in hunting. The most important feature in the definition of an ongon is the food: the spirit remains within as long as it is fed. Therefore the stone statues can also be included in the category of ongon.

INHABITED STATUES

As a consequence, Mongol effigies generally belong to the category of "inhabited portrait," that is, images serving as a support for the soul. Human representation was restricted to a few powerful personalities and was the object of a certain number of precautions and prohibitions. It was never used in less important contexts, such as decoration. In Ordos traditions, "a man's representation was regarded to be the man himself. To get hold of a drawing or a photograph of someone would give magic power over him." 13 Effigies used as a substitute for the ill person, or for the spirit of the illness, were made for healing rituals in connection with a ceremony for ransoming from death. 14 An animated statue can also act by itself and even kill. A thangka portrait of Chinggis Khan in a 17th-century description was said to kill if exposed or if denied proper sacrifices. 15 In the 15th century, it was said that the Western Mongol leader Togon Taishi 13 Antoine Mostaert, Dictionnaire Ordos (Peking: Catholic University, 1941-1944), 220b. 14 Charles R. Bawden, "The Supernatural Element in Sickness and Death According to Mongol Tradition. Part I," in Confronting the Supernatural: Mongolian Traditional Ways and Means (Wiesbaden: Otto Harrassowitz, 1994 [1961]), 237. 15 N. Hurcha, "Attempts to Buddhicize the Cult of Chinggis Khan," Inner Asia 1/1 (1999): 47. defied Chinggis Khan in front of his statue at the Eight White Tents in Ordos, and was inexplicably struck down. An arrow of the statue's golden quiver was found stained with blood and a wound looking like an arrow wound was discovered in his back. 16 To sum up, the Chinggisids worshipped personalized portraits of their ancestors by offering them sacrifices. The portraits served to legitimize and sacralize the ruling power, and were worshipped as gods. The spirit of the Mongol sovereign (süld) could also dwell in other supports, such as the standard, the relics (objects that once belonged to the Khan), the burial place, etc. These objects protected the state and helped to defeat its enemies. The possession of these supports (including the statues) and the ability to perform rites for them gave legitimacy and authority to the living Khan.

TWO-DIMENSIONAL PORTRAITS OF EMPERORS KEPT IN TEMPLES DURING THE YÜAN DYNASTY

Paintings of rulers cannot be directly fed, so they cannot be called ongon, but they are considered to be a support for an ancestor's soul. During the Yüan dynasty, Ancestors' temples (t'ai-miao 太廟) were built in the capital to enshrine tablets of the deceased emperors as well as two-dimensional portraits, 17 and painted portraits of Mongol emperors were also placed in the Han-lin-yüan 翰林院. 18 The Mongol emperors therefore adopted an ancestor cult based on Confucian lines. 19 During the reign of Emperor Ch'eng-tsung 成宗, ancestral shrines called Halls of Imperial Portraiture (first called Ying-t'ang 影堂, and then Shen-yü-tian 神御殿 or Yüjung-tian 御容殿) were built not as independent temples, but within the main imperial Buddhist monasteries of Beijing (such as the Ying-t'ang in the monastery of the Ta-shengshou wan-an-szu 大聖壽萬安寺 built by Temür for Khubilai and Jingim/Chen-chin 真 金). 20 After an emperor died, his own Ying-t'ang was installed for him and his ancestors in the temple he had built. Buddhist and sacrificial rites to the deceased emperor and empress were performed in front of these portraits. 16 Sagang Sechen 薩 囊 彻 辰 , Erdeni-yin Tobci, 1662, Urga manuscript, 102 fol., Gō Minoru, Igor de Rachewiltz, John R. Krueger and B. Ulaan (eds.), Erdeni-yin Tobci ('Precious Summary'): A Mongolian Chronicle of 1662, vol. I. (Canberra: The Australian National University, 1990), fol., 53 v°-54 r°. 17 Yüan-shih, chüan 74, Chi-szu 祭祀 3, Tsung-miao 宗廟 (Beijing: Chung-hua Shu-chü, 1976), 1370, 1831 sq. 18 "Preface," in T'u-hui Pao-chien 圖繪寶鑑, ed. Hsia Wen-yen 夏文彥 (Shang-yü-lo-chen-yü 上虞罗振玉, 1914), 1365, chüan 5: 4a sq; Yüan-shih, chüan 75, Chi-szu 4, Shen-yü-tien 神御殿, 1876. The portraits commissioned by Khubilai Khan, who ordered court painters to make a portrait of his son and heir apparent Jingim/Chen-chin 真金 and portraits of Chinggis Khan and his sons Ögödei 窩闊臺, and Tolui 拖雷, are the earliest recorded portraits. 19 Paul Ratchnevsky, "Über den Mongolischen Kult um Hofe der Grosskhane in China," in Mongolian Studies, ed. Louis Ligeti (Amsterdam: Grüner, 1970), 417-443. 20 Yüan-shih, chüan 75, Chi-szu 4, Shen-yü-tien, 1875.

Isabelle Charleux, "On Worshipped Ancestors and Pious Donors" Authors' own file, not the published version Please see the published version in National Palace Museum Bulletin, 40 (Dec. 2007), p. 17-36 6 Portraits of the past emperors and their consorts called yü-jung 御容 were kept in the Ying-t'ang. These portraits were of large dimensions: 245x210 cm (9.5x8 ft in Yüan measures). They were made from textile (usually k'e-szu 刻絲), an innovation that was highly valued but extremely costly and difficult to make. Khubilai's woven portrait, commissioned after his death by Temür in 1294, took more than three years to complete. 21 The chapter on paintings and sculpture in the Handbook of Governing (Ching-shih-ta-tien 經世大典) records several orders for portraits to be painted and converted to woven silk. The large portraits of emperors and empresses have not been preserved. But a painted album that could have served as the model for enlarged portraits has been preserved: Portraits of the Yüan Emperors and Empresses (Yüan-tai ti-hou-hsiang 元代帝 后像; now in the National Palace Museum; Figs. 3A-3B). Although the models in the album are half-length, the enlarged, finished portraits were full figures in a seated position (on a chair?) destined for the Ying-t'ang. The art historian Ching An-ning 景安寧 believes that the portraits of Khubilai and Chabi on the Taipei album may have been original works by the Nepalese artist Arniko (A-ni-ke 阿尼哥, 1245-1306). 22 The later portraits have been done in a similar style, by Chinese artists, such as Li Hsiao-yen 李肖岩 for the faces, and lesser craftsmen for the hats, hair and robes. The costumes, hats and hair braided into loops are all characteristic of the Yüan dynasty. 23 Other isolated half-length portraits that have been preserved, include a portrait of Chinggis Khan rediscovered in the Beijing History Museum in 1953, 24 and a portrait of Khubilai from a 13th century original preserved in the Confucius Temple at Ch'ü-fu 曲阜 (Shantung 山東 province). 25 These portraits, as well as the figure of Khubilai in the painting Khubilai Khan Hunting (Yüan-shih-tzu ch'u-lieh-t'u 元世祖出獵圖), allow us to say that the likeness of the portrait was relatively important.

It is not known if the emperor's portraits were consecrated or not, but their location in the temple show that they were considered as something between Buddhist icons and Chinese ancestor paintings. The enlarged portraits were produced in triplicate and distributed to Buddhist monasteries across China as formal public displays of the sovereign's image. There was therefore a multiplication of two-dimensional images of deceased emperors, sculpture being apparently excluded. In the Ying-t'ang were also displayed thangka mandalas the same size as the individual imperial portraits, also in k'e-szu, and woven in the same imperial workshops as the portraits. 26 One of these mandalas -the Vajrabhairava mandala -has been preserved in The Metropolitan Museum of Art of New York (Figs. 4A-4B). In the bottom left and right corners of the thangka, two emperors (Tug Temür -Emperor Wen-tsung 文宗, r. 1329-1332, and his elder brother Khoshila who reigned briefly in 1329 as Emperor Ming-tsung 明宗) and their respective consorts, Budashiri and Babusha, are identified by Tibetan inscriptions.27

TWO-DIMENSIONAL PORTRAITS OF PRINCES DURING THE NORTHERN YÜAN (1368-1635)

Three temples preserve portraits of Mongol Khans of the Northern Yüan dynasty.

The first is a painting of donors in Maidariin juu (Mei-tai-chao 美岱召), west of Hohhot 呼 和 浩 特 , where the Chinggisid nobility is represented below a 7-m high painting of Tsongkhapa on the west wall of the back shrine of the Assembly Hall (Fig. 5). 28 The two princesses who patronized this monastery -one of the oldest of the Buddhist revival -are both represented: on the right, Jönggen Khatun (known in Chinese as San-niang-tzu 三娘 子), Altan Khan's famous third wife (ca. 1550-1612) faces her third husband, who bends towards her in a respectful attitude (Fig. 6). On the other side of the painting, the princess Machag Khatun (or Uran Beiji, ca. 1546-1625) faces the Maidar Khutukhtu. Both princesses were identified as emanations of Green Tārā and White Tārā in the colophons of sutras' translations. They are surrounded by 58 laymen and monks of much smaller size and two divinities. The scene is laden with Buddhist symbols.

This painting provides evidence of the incontestable authority of San-niang-tzu and her legitimacy to rule the Tümed Mongols. It is at the same time a painting of Buddhist donors, a painting for the worship of San-niang-tzu as the emanation of a bodhisattva, and a commemorative, funerary painting. The temple preserved the funerary stupa of one of princesses (in the Ling-t'a-tian 靈塔殿).

Other thangka-like paintings of 16th-century nobles have been lost, such as a portrait of Altan Khan with his standard, and eight portraits of San-niang-tzu on hanging scrolls. It is important to notice that this painting covers only a small part of the south wall (to the right of the entrance) of the cave, which is dedicated to tutelary deities (yidam) and to Tibetan masters. Its location indicates that Chinggis Khan was not the main object of worship: Chinggis Khan, if it is him, is represented as a Buddhist lay donor (although it could also be a Tantric priest because of his three-fold crown). The conical hats, costumes and general style and composition suggest a much later date (Northern Yüan or Ch'ing dynasty).

In Cave 31 dedicated to Śākyamuni, monks and laymen are depicted under a painting of Vaiśravana to the left of the door. They also figure as Buddhist donors worshipping the Buddha on the north wall. Arjai was above all a Buddhist monastery, where Chinggis Khan may also have been worshipped.

PAINTINGS OF MONGOL RULERS IN THE CH'ING DYNASTY

Ch'ing dynasty Mongol portraits came under the influence of Sino-Manchu and Buddhist arts:

The religious portraits made of various materials (painting, silk appliqué, statuary, embalmed corpses) saw important developments, while the lay portraits were reduced to a few small donors at the bottom of the paintings.

The couple portraits of rulers disappear, sometimes replaced by Sino-Manchu-style individual ancestor portraits, such as the portraits of jasag lineages kept in the Ancestor Hall of their residence.

Thangka-like portraits of a few great ancestors are also found. Chinggis Khan, who was incorporated in the Buddhist pantheon during the 17th century as an incarnation of Vajrapāni and a son of Buddhist deities, is represented in the form of the deity Süld tengri.

Three Ch'ing dynasty "thangkas" deserve a special mention. The two first examples are Buddhist paintings; the third is strongly influenced by Tibetan Buddhist thangkas: Abatai Khan is represented at the centre of a thangka in an imaginary palace surrounded by miniature scenes from his life (Fig. 9). 31 Below him stands his monastery, Erdene Juu. The central figure and his attendants are in fact copied from the one of the above mentioned paintings of Abatai Khan at Erdene Juu. But here, Abatai has a vajratopped hat and holds lotuses that carry a sword and a vajra: the king is depicted with the attributes of a bodhisattva. His position, palace and courtiers mirror that of the king of Shambala in 19th-century thangkas. In a thangka, which is the main object of worship in the ancestors' shrine of Khutugtai Sechen khong taiji (1540-1586) and Sagang Sechen (1604-?) in Ordos (now in Shan-hsi 山西 province), Chinggis Khan is depicted as a fierce protective deity, topped by three lamas (Fig. 10). Below him stands Khutugtai Sechen khong taiji, and on the right, breaking the general symmetry, sits Sagang Sechen, the author of the Erdeni-yin Tobci (Meng-ku yüan-liu 蒙古源流), smaller than his grandfather. The distinction between the fierce dharmapāla Chinggis Khan surrounded by flames, and his two famous descendants, depicted as motionless human-like ancestors, is striking.

A vertical painting of the imperial family, said to be a copy of a late Yüan painting preserved in the Chinggis Khan Mausoleum at Ejen Khoroo 伊金霍洛旗, Ordos (Fig. 11), represents Chinggis Khan with his main wife surrounded by sons or courtiers. Because of the thangka format, the individual thrones with headboards, the Buddhist halo, the Buddhist-style offerings such as jewels, and the hats and costumes so different from Yüan models, this painting can probably be dated from the Ch'ing dynasty.

BETWEEN ANCESTORS AND WORSHIPPING DONORS

The Mongol sovereigns were depicted in three different roles:

As the main subjects of the painting, they are depicted alone (Figs. 3A-3B), surrounded by courtiers, servants or sons presenting offerings (Fig. 11); or in the middle of a complex thangka (Fig. 9). This last example showed that Buddhism played a prominent role in legitimizing Mongol rule: Abatai Khan is explicitly depicted with the specific attributes of a bodhisattva, and recalls the thangkas of the emperor Ch'ien-lung, depicted as an emanation of the bodhisattva Mañjuśrī.

As Buddhist donors, they are depicted in a three-quarters view, turned towards a larger painting of Buddha. They are of small size, often at the bottom of the painting. This is a classical subject in Buddhist painting, long before the Mongols appeared. In Mo-kao caves at Tun-huang (Cave no. 332) for instance, Yüan dynasty Mongol donors are painted on both sides of the entrance, lined up behind each other, and facing the main Buddha image. These portraits commemorate their donations, showing their generosity to the public. In the mandala of Vajrabhairava, in contrast with the large imperial portraits, the emperors are represented as very small-scale worshippers, joining their hands in prayer, on the same level as the dharmapāla, under a large Buddhist figure (Figs. 4A-4B).

In a third category, the Mongol Khan appears as a Buddhist donor in the bottom of a larger Buddha image, and at the same time as an ancestor worshipped by smaller characters. He adopts the frontal position of the cakravartin king, and the monks are in a position of inferiority in relation to the Chinggisid aristocracy.

In Maidaiin Juu, San-niang-tzu sits in a frontal position. Her jewellery, the yellow colour of her robe, her large earlobes, the amrita vase she holds, and the two small monks on her sides evokes a bodhisattva or a Buddha (Fig. 7). The location of the donors' painting at the same level as the viewer's eyes, as well as its large size (16x2 m), shows the donors' importance. The main character of the Arjai painting in Cave 28 sits frontally; the others, slightly turned towards him, make the worshipping mudrā (anjali mudrā; Fig. 8). The painting of Abatai Khan at Erdene Juu was probably located under a larger painting of Buddha: in one of the scenes, 10 men pay homage to what was probably a Buddha or a divinity, sitting or kneeling in a respectful attitude, presenting cups full of offerings. Abatai and his wife are the only frontal characters. In Fig. 10, Khutugtai Sechen is depicted as a divinized ancestor but his location below the divinized Chinggis Khan makes him a kind of emanation of Chinggis Khan, while Sagang Sechen discreetly stays in the background.

The iconic frontal representation and size of these Northern Yüan and Ch'ing ancestors-donors seems to be an innovation in Buddhist painting, and contrasts with the usual three-quarters posture of Central Asian, Chinese and Tibetan donors, as seen in the Tun-huang and Turfan caves, the temples of Western Tibet (of Ku-ke 古格), and in Tibetan thangkas.

THE ENTHRONED COUPLE

The Mongols made eclectic choices when representing their rulers, borrowing themes from the Chinese, Turkic, Uyghur and other traditions, and rejecting others. For instance, the Mongols of East Asia chose not to represent their monarch on horseback, in contrast to Turkic kings, a theme taken over by the Ilkhanid rulers as can be seen in the book-paintings from the Ilkhanid period. The Mongol king wears no weapons and is shown enthroned, peacefully ruling his empire. Unlike the Turkic stone men, the Mongol stone figures are unarmed.

The Khan is often painted on a throne with his main wife. The Khatun has the same size and sits on an equal footing with the Khan. It shows the importance of the couple, or of the whole family dominated by the couple, depicted as equals. A similar arrangement, found in Ilkhanid manuscript paintings, shows the enthroned king with his queen in an open air courtly reception, especially in the Jami 'al-tavarikh by Rashīd ad-Dīn (Figs. 12-13). The representation of couples is also found in several Yüan tomb paintings uncovered in northern China and Inner Mongolia (Figs. 14-15). These portraits of the tomb occupants At court as well as in the yurt, Mongolian women traditionally sat to their husband's left, the right being the honorific In the Taipei album, the emperors' faces are slightly turned to the right and the empresses' faces to the left, so we can assume that the emperors and empresses portraits were hung side by side or facing each other, forming an equal pair, the wife seated at her husband's left (Figs. 3A-3B).

The reverse, seen in two tomb murals (San-yen-ching 三眼井, Ch'ih-feng 赤峰 Municipality, Inner Mongolia, and Pei-yü-k'ou 北峪口, Wen-shui 文水, Shan-hsi), seems to be an "anomaly," probably a Chinese influence. In a political document depicting Altan Khan and his wife (probably San-niang-tzu), the Khatun sits on the Khan's right (Fig. 16). 32 The switched position might have been intended to fit with Chinese customs, and to please the Ming emperor. Or the letter was rewritten and redrawn by the Ming officials before being presented to the emperors, as was usual for this kind of document. In other cases, the position of power of a woman such as San-niang-tzu, or her great age, can reverse the usual gender position. A related question is the fastening of garments on the right that served as a basic ethnic marker distinguishing Mongols from Chinese. But why choose to paint the couple to represent the Khan's power? The explanation can be found in the role of women in Mongol society and in the conception of power. The Mongol queens enjoyed a certain authority, independence and privileges, appeared in public with the ruler, participated in feasts and took part in the assemblies. A few "remarkable women" of the imperial family, especially widows, played a decisive role in Mongol politics, or even ruled the domain (such as Töregene Khatun, and, later, Sanniang-tzu). Their representation on the throne could be the recognition of their political influence. It must be noted that although the majority of Mongol rulers were polygamous, only one spouse is usually depicted: the first wife sat on the throne with her husband in official banquets. Only the Arjai Cave 28 and Hou-te-sheng 後德勝 Tomb (Liang-ch'enghsien 涼城縣 district, Inner Mongolia) paintings show the Khan with several wives. I have another interpretation: it seems that a double, diarchic principle, male and female, is inherent in the representation of power in the Mongolian world, as it is in the supernatural world (as seen in the binary figures of deities, such as the two complementary ancestors Bulagat and Ehirit of the Buriats, or the Gods of the left and right wings in the old pantheon). The portraits of couples disappear after Mongolia is incorporated within the Sino-Manchu Empire.

FROM THE THREE-QUARTERS VIEW TO THE FRONTAL VIEW

In 13th-15th century portraits, the ruling couple is depicted in a three-quarters view, looking at each other. They often adopt a relaxed position, asymmetric and nonchalant that conveys familiarity and humanity. 33 In Ilkhanid manuscripts and Yüan tomb paintings (Figs. 12-15), 34 the main characters have their hands on the knees, or one arm rests on the armchair; legs are open, or one of the legs is slightly folded, a posture close to the "royal ease posture" from Buddhist paintings of kings. They generally sit on a folding chair (chiao-i 交椅) -a symbol of prestige and power in Chinese society -favoured by the Mongol nomadic elite.

Post-Yüan portraits show a frontal view that can be called "a rigid iconic posture" (Figs. 5-11). The frontal view is certainly an influence of Buddhist painting, because it appears along with a profusion of Buddhist attributes and objects (halos, khatag, ritual scarves, jewels, eight auspicious symbols, wish-granting jewels, cintāman i, etc.). The frontal posture shows that the main characters are worshipped as Buddhas (especially when they have a halo) and/or as ancestors. Power seems to be more impersonal and strict. They generally sit cross-legged on a throne or on a cushion: in Buddhist Mongolia, the crosslegged position is the most honorific posture.

Secondary figures, depicted in small dimensions following the principle of "hieratic scale" in Buddhist art, can either be sons, courtiers, servants, and/or worshippers. They adopt a posture of humility expressing deference or subordination: standing or kneeling to offer a gift in a three-quarters posture. They join their hands in worshipping, present a jewel, hold Buddhist symbols, and play music.

THE CUP, THE STANDARD, AND OTHER OLD SYMBOLS OF ROYAL POWER

The standard, one of the main symbols of power in the Mongolian world believed to embody the soul of the Khan, is seen in one of Abatai Khan's painting in Erdene Juu and in the painting of Chinggis Khan and Khutugtai Sechen khong taiji (see bottom left, where four standards surround a fifth one; Fig. 10). In the paintings of Ejen Khoroo (Fig. 11) and Erdene Juu, attendants holding a quiver with arrows, a bow and a horse, are reminiscent of ancient Türkic compositions. Bows, arrows and quivers were also symbols of royal power in the Türkic world (but are never seen in the sovereign's hands). These paintings seem to be representative of an ancient style. But these ancient symbols are mixed with Buddhist symbols in Buddhist or thangka-like paintings.

The Mongol sovereign often holds a cup or a bowl at breast level, raises the cup to drink it, or offers it to his Khatun (Figs. 1, 11). The cup seems to be the most characteristic non-Buddhist attribute. It is linked with the fact that the couple receives a cult and is fed.

The stone men's cup belongs within a funerary context and is obviously a heritage of the Türkic period. Corpses were also found with a cup near their hand in tombs. The stone men's cup is thought to contain (symbolically or materially) alcohol, water, or perhaps offerings of fat, burnt meat. It may be an allusion to the funerary banquet given to the deceased.

Alcohol is a fundamental element of Mongol rituals: libations are offered in cups to feed the spirits, gods, and ancestors. Sprinklings made towards Heaven and the four cardinal points remain a daily gesture of rural Mongols. At the end of a sacrifice, after the offering of alcohol and meat, they are shared and consumed by the participants (see the sacrifice to Chinggis Khan at Ejen Khoroo). Receiving a share of meat and drink means that the participants are securing the blessing of the ancestors or of the divinity.

The cup in the hands of a monarch in regalia (on a throne) also evokes the "cuprite" performed in enthronement ceremonies, in the investiture of a vassal (oath of allegiance), and (blood brotherhood of unrelated men in an equal relationship), and wedding rituals in the Inner-Asian nomadic world since 1000 CE. 35 The "communion" (drinking the same beverage at the same time) seals a contract between two parties (alliance, marriage) or between a king and his subjects. In Mongol paintings, cups are also raised by courtiers paying homage to the monarch. The gesture of offering a cup, and the kneeling posture, meant servitude, acceptance of vassalage, and worship. So here, funerary rites and worshipping rites paralleled the cup-rite of royal ceremonies; these distinct ceremonies visually converge in commemorative paintings where enthroned kings and queens are worshipped as ancestors. But with the 16th-century Buddhist renaissance, the cup, at least in the Khan and the Khatun's hands, is often replaced by a Buddhist attribute such as a khatag (Fig. 7), a rosary (Figs. 5, 17) or a cintāman i (Fig. 5).

Fig. 2 .

 2 Fig. 2. Three ongon, bronze (5 cm, 4,8 cm and 4.3 cm), Mongol Empire, excavated in T'ung-liao 通 遼 Municipality, Inner Mongolia. From: Ta-han Te Shih-chieh: Meng-yüan Shih-tai Te Toyüan Wen-hua Yü I-shu 大汗的世界:蒙元時代的多元文化與藝術, eds. Shih Shou-ch'ien 石 守謙 and Ko Wan-chang 葛婉章 (Taipei: National Palace Museum, 2001)

Fig. 3A .

 3A Fig. 3A. Portrait of Khubilai Khan, album leaf, ink and color on silk, 59.4x47 cm, China, Yüan dynasty, from Portraits of the Yüan Emperors (Yüan-tai Ti pan-shen-hsiang 元代帝半身像), Collection of the National Palace Museum, Taipei Fig. 3B. Portrait of Chabi, album leaf, ink and color on silk, 61.5x48 cm, China, Yüan dynasty, from Portraits of the Yüan Empresses (Yüan-tai ti-hou pan-shen-hsiang 元代 帝 后 半 身 像 ), Collection of the National Palace Museum, Taipei

Fig

  Fig. 4A and 4B. Mandala of Vajrabhairava, k'e-szu, 246.1x208.3 cm, China, ca. 1328-29 or after 1332, The Metropolitan Museum of Art of New York (Purchase, Lila Acheson WallaceGift, 1992 (1992.54). Detail: two emperors, Tug Temür and Khoshila, on the lower left of the thangka and their respective consorts Budashiri and Babusha on the lower right.

Fig. 5 .

 5 Fig. 5. Mural painting representing Buddhist lay donors and monks of Altan Khan's family, main temple of Maidariin Juu, H: 2 m, L: 16 m, 17th century. © Chin Shen

Fig. 9 .

 9 Fig. 9. Abatai Khan, central part of a cloth thangka, unknown painter, 62x86 cm, Central Museum, Ulan-Bator

Fig. 10 .

 10 Fig. 10. Thangka worshipped at Sasa (Ta-fen-t'an 大 墳 灘 ), Üüsin banner, now in Shanhsi province. It represents Chinggis Khan as a dharmapāla, below are Khutugtai Sechen khong taiji and Sagang Sechen. From Qasbiligtü C. and M. Qasbaγan-a, Ordos-un soyol-un öb, Baotou: Yi meng minjian wenxue yanjiuhui, 1987.

Fig. 11 .

 11 Fig. 11. Chinggis Khan, his main consort and his family. Copy of a Yüan dynasty painting preserved in the Mausoleum of Chinggis Khan, Ejen Khoroo banner, Ordos (probably Ch'ing dynasty). From Walther Heissig, "Les religions de la Mongolie", in Giuseppe Tucci and Walther Heissig, Les Religions du Tibet et de la Mongolie, transl. from German by R. Sailley, Paris: Payot, 1973 (Les Religions de l'humanité) [Stuttgart, 1970]: 421, fig. 11 (from Dylykov, S. D.,

Fig. 12 (

 12 Fig. 12 (left). Enthronement scene depicting the ruler and his consort surrounded by members of the court, detail, Jami 'al-tavarikh (Compendium of Chronicles) by Rashīd ad-Dīn, illustration from the Diez Albums, ink, colors and gold on paper, Iran (possibly Tabriz), early 14th century, Staatsbibliothek zu Berlin -Preussischer Kulturbesitz, Orientabteilung (Diez A fol. 70, S. 10)

Fig. 16 .

 16 Fig. 16. Altan Khan and his wife in a yurt in front of Hohhot and the Ta-chao 大召 (Hung-tz'uszu 弘慈寺), painting which accompanied a letter written on a horizontal scroll, dated August 17, 1580, addressed to the Ming emperor. Institute of Eastern Studies, attached to the Russian Academy of Sciences, St. Petersburg. © Isabelle Charleux

D. Zélénine, Le Culte des Idoles en Sibérie, translated from Russian by G.Wetter (Paris: Payot, 1952 [1936]), chap. 5.

Yüan-shih, chüan 134, Lieh-chüan 列傳: T'ang Jen-tzu 唐仁祖, 3253-3254. Isabelle Charleux, "On Worshipped Ancestors and Pious Donors"

Jing Anning (Ching An-ning), "The Portraits of Khubilai Khan and Chabi by Anige (1245-1306), a Nepali Artist at the Yüan Court," Artibus Asiae, 54:1/2 (1994): 40-86.

Yü Hui 余輝, "Yüan-tai Kung-t'ing Hui-hua-shih Chi Chia-tso K'ao-pien 元代宮廷繪畫史及佳作考辦:

Yüan-tai Hua-su Chi 元代畫塑記 (Beijing: Jen-min Mei-shu Ch'u-pan-she, 1964), 1.

James C. Y. Watt and Anne E. Wardell, When Silk Was Gold: Central Asian and Chinese Textiles (New York: The Metropolitan Museum ofArt, 1997), 95-100, cat. no. 25.

Isabelle Charleux, "La Peinture des Donateurs du Temple de Maitreya en Mongolie Méridionale," Arts Asiatiques 54 (1999): 85-102.

Isabelle Charleux, "On Worshipped Ancestors and Pious Donors"

Aleksej M. Pozdneev, "Novo-otkrytyj Pamjatnik Mongol'skoj Pis'mennosti Vremen Dinastii Min," Vosčnye Zametky 14 (1895): 367-381; Isabelle Charleux, Temples et Monastères de Mongolie-Intérieure (Paris: Comité des Travaux Historiques et Scientifiques & Institut National d'Histoire de l'Art, 2006), 48-49.

See also the illustration in Shih-lin Kuang-chi 事林廣記, ed. Ch'en Yüan-ching 陳元靚, vol. 2 (Beijing :Chung-huaShu-chü, 1963Shu-chü, ), 1330Shu-chü, -1333. .

Robert Hillenbrand, "The Arts of the Book in Ilkhanid Iran," in The Legacy of Genghis Khan: Courtly Art and culture in WesternAsia, 1256-1353, eds. Linda Komaroff and Steffano Carboni (New York: The Metropolitan Museum of Art, 2002), 134-167.

We know that traditions from the Mongolian court of China may have made their way at Central Asia through book-printing.

Isabelle Charleux, "On Worshipped Ancestors and Pious Donors" 35 Robert Bleichsteiner, "Zeremonielle Trinksitten und Raumordnung bei den Turco-mongolischen Nomaden," Archiv für Völkerkunde VI-VII (1951-1952): 181-208, p. 192 sq.; Emel Esin, "The Cup Rites in Inner-Asian and Turkish Rites," in Forschungen zur Kunst Asiens: in Memoriam Kurt Erdmann, ed. Oleg Grabar (Istanbul: Istanbul üniversitesi edebiyât fakültesi, 1969), 224-261. Isabelle Charleux, "On Worshipped Ancestors and Pious Donors"

Authors' own file, not the published version Please see the published version in National Palace Museum Bulletin, 40 (Dec. 2007), p. 17-36 Authors' own file, not the published version Please see the published version in National Palace Museum Bulletin, 40 (Dec. 2007), p. 17-36 Authors' own file, not the published version Please see the published version in National Palace Museum Bulletin, 40 (Dec. 2007), p. 17-36 Authors' own file, not the published version Please see the published version in National Palace Museum Bulletin, 40 (Dec. 2007), p. 17-36 Authors' own file, not the published version Please see the published version in National Palace Museum Bulletin, 40 (Dec. 2007), p. 17-36 Authors' own file, not the published version Please see the published version in National Palace Museum Bulletin, 40 (Dec. 2007), p. 17-36 10

The second example is a series of three paintings of Abatai Khan (1554-1588), the Tüüshet Khan of Khalkha Mongolia, painted on a wall at Erdene Juu monastery (in present-day Mongolia). They are known from copies made by Dendev in 1950 (Fig. 7): the originals have not been preserved. 29 The Khan is depicted sitting cross-legged alone, or with his wife, and receiving the homage of monks and laymen. Abatai Khan, the founder of the monastery (1585-1586?), was buried there: Erdene Juu, like Maidar Temple, became a funerary shrine after the death of its founder. His large tent preserving his throne, weapons, and statues was worshipped there (and later transferred to Khüree). A third example comes from the Arjai Caves 阿爾寨石窟 (Pai-yen-yao shih-k'u 百 眼窯石窟) in Otog banner in Ordos territory. The caves were decorated since the Northern Wei 魏 dynasty (386-534), and were probably a Hsi-hsia 西夏 monastery before the Mongol conquest. A painting allegedly representing Chinggis Khan's family in Cave 28 caused much ink to flow (Fig. 8). The Chinese archaeologists imagine Arjai as a major Chinggisid sacrificial site under the Yüan dynasty, perhaps a shrine to perform rituals for Chinggis Khan. The painting of Cave 28 would be comparable to an imperial portraiture (yü-jung) for the sacrificial rites. 30 It is believed to represent Chinggis Khan surrounded by his main wife (on his right), his two concubines (on his left) and his four sons (farther on his left). In front of them is a table full of offerings. A hundred lay worshippers in procession bend or kneel towards the altar.

CONCLUSION

As in medieval Europe, the portrait developed from funerary statues to a political and religious symbol linking the past sovereign to the present ruler. Sculpted portraits were supports for the soul, used to feed and worship the ancestors. Under the Buddhist influence of Khubilai's reign, the ongon were replaced by painted and woven portraits, and statues were reserved for Buddhas and holy lamas.

The evolution of these portraits reveals the convergence between traditional beliefs in the deceased protector ancestors, the importance of family and clan, Chinese-style ancestor worship, and Buddhist ideas of a cakravartin ruler. Chinggis Khan was worshipped first as an ancestor, then as a deity, and later forcibly integrated into the Buddhist pantheon. Other Mongol rulers were represented as bodhisattvas and donors at the same time. The various meanings of the rulers' portraits were often interwoven: commemoration, veneration of a divinized ancestor, legitimization of a living ruler through his ancestors' portraits, and exaltation of the devotion of Buddhist donors.

Originally created to serve the ancestor worship of their descendants, once exposed within Buddhist monasteries, they became relatively public objects exposing the Khan's power, domination and privileges to visitors' eyes. The Ilkhanid illustrated manuscripts exalting the history of the Mongols such as the Jami 'al-tavarikh also had political and propagandist aims. 36 The ancient Inner Asian heritage of frontal representation and cup-rites had to compete with three-quarters and relaxed postures and with Buddhist attributes. But in any case, the Mongols chose a pacific representation of the sovereign, with his main wife, and often his whole family. These portraits also give us much information on selfrepresentation, costume, gender status, ancestor worship and conventions, reflecting the highly personalized nature of politics for Mongols.


Christian Mougin

René Scalla

Ferdinand Cabanne

Occurrence of cytochrome P-450 mono-oxygenases in the metabolism of chlorotoluron by wheat microsomes

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


A De Mones

Alexis Fostier Characterization

Characterization and GtH regulation of microsomal ovarian aromatase activity in rainbow trout


Florence Le Gac

teaching and research institutions in France or abroad, or from public or private research centers.

Evolution of sensitivity to GtH and GtH receptors in

the trout testis (Salmo gairdneri)


Alexis Fostier

Florence Le Gac

Maurice Loir

Maurice Loir Steroids

à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.


F Le Menn

Jesus Nunez Rodriguez

Bernard Breton

P Copeland

Incorporation of vitellogenin in fish

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


Anne Bouillard -Sidney

Rosario -Albert Benveniste

Stefan Haar

Anne Bouillard

Sidney Rosario

Albert Benveniste

† S Rosario

Monotony in Service Orchestrations

Keywords: web service, orchestrations, contracts, monotony web service, orchestrations, contrats, monotonie

Web Service orchestrations are compositions of different Web Services to form a new service. The services called during the orchestration guarantee a given performance to the orchestrater, usually in the form of contracts. These contracts can be used by the orchestrater to deduce the contract it can offer to its own clients, by performing contract composition. An implicit assumption in contract based QoS management is: "the better the component services perform, the better the orchestration's performance will be". Thus, contract based QoS management for Web services orchestrations implicitly assumes monotony.

In some orchestrations, however, monotony can be violated, i.e., the performance of the orchestration improves when the performance of a component service degrades. This is highly undesirable since it can render the process of contract composition inconsistent.

In this paper we define monotony for orchestrations modelled by Colored Occurrence Nets (CO-nets) and we characterize the classes of monotonic orchestrations. We show that few orchestrations are indeed monotonic, mostly since latency can be traded for quality of data. We also propose a sound refinement of monotony, called conditional monotony, which forbids this kind of cheating and show that conditional monotony is widely satisfied by orchestrations. This finding leads to reconsidering the way SLAs should be formulated.

Introduction

Web Services and their compositions are being widely used to build distributed applications over the internet. Web Service orchestrations are compositions of Web Services to form an aggregate, and usually more complex, Web Service (WS). The services involved in a WS orchestration may have widely different behaviour (both functional and non-functional) and may be separated geographically by large distances.

A WS orchestration is itself a Web Service, and it can be further composed with other Web Services to build increasingly sophisticated services. The functioning of such service compositions can thus be quite complex in nature. There is a need to formally describe these systems in order to be able to build and reason about them. Different formalisms have been proposed for this purpose, the most popular amongst these is the Business Process Execution Language (BPEL) [START_REF] Andrews | Business Process Execution Language for Web Services Version 1.1. Specification[END_REF] a standard proposed by Microsoft and IBM. Another formalism is Orc [START_REF] Misra | Computation orchestration: A basis for wide-area computing[END_REF] a small and elegant formalism equipped with extensive semantics work [START_REF] Kitchin | A language for task orchestration and its semantic properties[END_REF][START_REF] Rosario | Event structure semantics of orc[END_REF]. Various models exist, that have been either used to model directly orchestrations or choreographies, or as a semantic domain for some formalisms. Noticeably Petri Nets based models, e.g., WorkFlow Nets [START_REF] Van Der Aalst | The Application of Petri Nets to Workflow Management[END_REF][START_REF] Wil | Verification of workflow nets[END_REF] and process algebra based models.

The main focus of the existing models is to capture the functional aspects of such compositions. However, non-functional -also called Quality of Service (QoS) -aspects involved in services and their compositions need also to be considered. The QoS of a service is characterised by different metrics, for e.g., latency, availability, throughput, security, etc. Standard WSLA [START_REF] Keller | The wsla framework: Specifying and monitoring service level agreements for web services[END_REF] specifies how QoS can be specified using Service Level Specifications and Agreements. Examples of SLA parameters are found in this document that illustrate the current practice. In particular, "conditional SLA obligations" consist in specifying what a service must guarantee given that the environment satisfies certain assumptions.

QoS management is typically based on the notion of contract. Contracts are agreements made between the orchestrater and the different actors (the called services) involved in the orchestration. Contracts formalise the duties and responsibilities each subcontractor must satisfy. For e.g., a service which is called in an orchestration can have a contract of the type : for 95% of the requests the response time will be less than 5ms. All these contracts with the services involved in the orchestration could then be composed by the orchestrater to help it propose its own contract with users of the orchestration. This process is called contract composition.

In [START_REF] Rosario | Probabilistic QoS and soft contracts for transaction based web services[END_REF] we introduced the notion of probabilistic contracts to formalise the QoS behaviour of services -the work of [START_REF] Rosario | Probabilistic QoS and soft contracts for transaction based web services[END_REF] focused on latency. We showed how these contracts can be composed to get the end-to-end orchestration's contract. We also showed that realistic overbooking of resources by the orchestrater is possible using this approach.

Contract based QoS management relies on the implicit assumption that, if each sub-contractor meets its contract objectives, then so does the orchestrater. Vice-versa, a sub-contractor breaching its contract can cause the orchestrater to fail meeting its overall contract objectives. Thus the whole philosophy behind contracts is that the better sub-contractors behave, the better the overall orchestration will meet its own contract. In fact, the authors themselves have developed their past work [START_REF] Rosario | Probabilistic QoS and soft contracts for transaction based web services[END_REF] based on this credo. . . until they discovered that this implicit assumption could easily be falsified. Why so?

S T N M

Figure 1: A non-monotonic orchestration As an illustration example, consider the orchestration in Figure 1. Services M and N are first called in parallel. If M responds first, service S is next called and the response of N is ignored. If N responds first, T is called and not S. Let δ i denote the response time of site i. Assume the following delay behaviour : δ M < δ N and δ S ≫ δ T . Since M responds faster, the end-to-end orchestration delay d 0 = δ M + δ S . Now let service M behaves slightly 'badly', i.e delay δ M increases and becomes slightly greater than δ N . Now service T is called and the new orchestration delay is

d 1 = δ N + δ T . But since δ S ≫ δ T , d 1 is in fact lesser than d 0 .
This orchestration is non-monotonic since increasing the latency of one of its components can decrease the end-to-end latency of the orchestration. So, what is the nature of the difficulty?

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"Simple" composed Web services are such that QoS aspects do not interfere with functional aspects and do not interfere with each other. Their flow of control is typically rigid and does not involve if-then-else branches. For such cases, latencies will compose gently and will not cause pathologies as shown above. However, as evidenced by the rich constructions offered by BPEL, orchestrations and choreographies can have branching based on data and QoS values, various kinds of exceptions, and timers. With such flexibility, non-monotony such as that exhibited by the example of Figure 1 can very easily occur.

Lack of monotony, in turn, impairs using contracts for the compositional management of QoS. Surprisingly enough, this fact does not seem to have been noticed in the literature.

In this paper we give a classification for orchestrations based on their monotonic characteristics. Our study focuses on latency, although other aspects of QoS are discussed as well. This paper is organised as follows: Section 2 informally introduces the notion of monotony with examples. In section 3 we recall the definition of Petri nets and colored Petri nets, and introduce our model, OrchNet. A formal definition of monotony and a characterisation of monotonic orchestrations is then given in section 4. Section 5 introduces conditional monotony which will be useful to deal with non-monotonic orchestrations which use data-dependent control.

Non-monotonic patterns in CO-nets

We now show examples of non-monotonic orchestrations and identify the source of their non-monotony. The necessary and sufficient conditions for monotony that we give later were inspired from the study of these patterns. The examples we discuss here informally use Petri nets; we believe they are self-explanatory and do not deserve formal definitions. The formal definitions of Petri nets and their semantics is given in section 3.

Consider the net on Figure 2 The overall latency here is max(τ a + τ d , τ c + τ f ) = 5 + τ * . We thus see that for this net to be monotonic, we must have the latencies of the concurrent transitions a and c to be the same (along with their futures). In fact, since τ a = τ c and τ d = τ f , the two concurrent branches can be "folded" into a single branch to give us a net similar to that of A monotonic orchestration: Figure 4 shows an orchestration that has a fork-join pattern (in the left). The right side of the figure shows the net's unfolding. (The unfolding of a net N is an acyclic net which includes all the possible executions of N . Every place in the unfolding can be marked by at-most one transition and so every possible way of enabling a transition is distinguished. In Figure 4, the two possible cases in which event c can be fired are distinguished in the unfolded net). Since the left net has a choice pattern, one may think that it is not monotonic. However, this is not true. From the previous example we know that the unfolded net is monotonic since the futures of the conflicting transitions a and b are the same (and hence have the same latencies). At this point we have identified good and bad patterns for monotony. Going beyond such simple findings proved to be surprisingly challenging. In particular,

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characterizing that the restricted class of orchestrations we define is a necessity for monotony is demanding. All this requires more formal material that we introduce next.

The Orchestration Model: OrchNets

In this section we present the orchestration model that we use for our studies, which we call OrchNets. OrchNets are a special form of colored occurrence nets (CO-nets), which are high level Petri Nets.

We have chosen this mathematical model for the following reasons. From the semantic studies performed for BPEL [START_REF] Ouyang | Formal Semantics and Analysis of Control Flow in WS-BPEL[END_REF][START_REF] Arias-Fisteus | Applying model checking to BPEL4WS business collaborations[END_REF] and Orc [START_REF] Kitchin | A language for task orchestration and its semantic properties[END_REF][START_REF] Rosario | Event structure semantics of orc[END_REF] we need to support in an elegant and succinct way the following features: concurrency, rich control patterns including preemption, and for some cases even recursion. The first two requirements suggest using colored Petri nets. The last requirement suggests considering extensions of Petri nets with dynamicity. However, in our study we will not be interested in the specification of orchestrations, but rather in their executions. Occurrence nets are concurrent models of executions of Petri nets. As such, they encompass orchestrations involving recursion at no additional cost. The executions of Workflow Nets [START_REF] Van Der Aalst | The Application of Petri Nets to Workflow Management[END_REF][START_REF] Wil | Verification of workflow nets[END_REF] are also (CO-nets).

Petri nets, Occurrence nets

Definition 1 A Petri net is a tuple N = (P, T , F , M 0 ), where P is a set of places,
T is a set of transitions such that P ∩ T = ∅, F ⊆ (P × T ) ∪ (T × P) is a set of flow arcs, M 0 : P → N is the initial marking.

The elements in P ∪T are called the nodes of N and will be denoted by variables for e.g, x. For node x ∈ P ∪ T , we call

• x = {y | (y, x) ∈ F } the preset of x, and x • = {y | (x, y) ∈ F } the postset of x. A marking of the net is a multiset M of places, i.e a map from P to N. A transition t is enabled in marking M if ∀p ∈ • t, M (p) > 0. This enabled transition can fire resulting in a new marking M -• t + t • denoted by M [t M ′ . A marking M is reachable if there exists a sequence of transitions t 0 , t 1 . . . t n such that M 0 [t 0 M 1 [t 1 . . . [t n M . A net is safe if for all reachable markings M , M (p) ⊆ {0
, 1} for all p ∈ P. We define two relations on the nodes of a net: Definition 2 (Causality) For a net N = (P, T , F , M 0 ) the causality relation < is the transitive closure of the relation ≺ defined as:

If p ∈ • t, then p ≺ t, If p ∈ t • , then t ≺ p,
where p ∈ P, t ∈ T .

The reflexive closure of < is denoted by ≤. For a node x ∈ P ∪ T , the set of causes of x is ⌈x⌉ = {y ∈ P ∪ T | y ≤ x}. Definition 3 (Conflict) For a net N = (P, T , F , M 0 ) two nodes x and y are in conflict -denoted by x#y -if there exist distinct transitions t, t ′ ∈ T , such that t ≤ x, t ′ ≤ y and

• t ∩ • t ′ = ∅.
Nodes x and y are said to be concurrent -written as x y -if neither (x ≤ y) nor (y ≤ x) nor (x#y). A set of concurrent conditions P ⊆ P is called a co-set. A cut is a maximal (for set inclusion) co-set.

Definition 4 (Configuration) A configuration of N is a subnet κ of nodes of N such that: 1. κ is causally closed, i.e, if x < x ′ and x ′ ∈ κ then x ∈ κ 2. κ is conflict-free, i.e, for all nodes x, x ′ ∈ κ, ¬(x#x ′ )
For convenience, we will assume that the maximal nodes (w.r.t the < relation) in a configuration are places.

Definition 5 (Occurrence nets)

A safe net N = (P, T , F , M 0 ) is called an occurrence net (O-net) iff 1. ¬(x#x) for every x ∈ P ∪ T .
2. ≤ is a partial order and ⌈t⌉ is finite for any t ∈ T .

For each place p

∈ P, | • p| ≤ 1.
4. M 0 = {p ∈ P| • p = ∅}, i.e the initial marking is the set of minimal places with respect to ≤ N .

Occurrence nets are a good model for representing the possible executions of a concurrent system. Unfoldings of a safe Petri net, which collect all the possible executions of the net, are occurrence nets. Unfoldings are defined as follows.

For N and N ′ two safe nets, a map ϕ : P ∪ T → P ′ ∪ T ′ is called a morphism of N to N ′ if: 1/ ϕ(P) ⊆ P ′ and ϕ(T ) ⊆ T ′ , and 2/ for every t ∈ T and

t ′ = ϕ(t) ∈ T ′ , • t ∪ {t} ∪ t • is in bijection with • t ′ ∪ {t ′ } ∪ t ′ • through ϕ.
Now, for N a safe net, there exists pairs (U, ϕ) where U is an occurrence net and ϕ : U → N is a morphism -the places and transitions of U are "labeled" with places and transitions of N through morphism ϕ. The unfolding of N , denoted by (U N , ϕ N ) or U N for short, is the smallest pair (U, ϕ) with the above properties, where smallest refers to inclusion up to isomorphism. The configurations of U N are the executions of N , seen as partial orders of events.

Figure 5 shows a safe net N and a small part of its unfolding U N . A step in the construction of U N is shown in the figure on the right. In each such step, a set of concurrent conditions X in U N are chosen such that ϕ(X) = • t for some transition t in N . The set of nodes X ∪ {t ′ } ∪ t ′ • are then added to U N where ϕ(t ′ ) = t and ϕ(t ′ • ) = t • . The right figure shows the addition of a new copy of transition a (along with its preset and postset) to U N .

Any place of an occurrence net (specifically, an unfolding) gets a token atmost once. We can thus talk about "the token of the place" unambiguously for any place in these nets.

Our Model: OrchNets

We now present the orchestration model that we use for our studies, which we call OrchNets. OrchNets are occurrence nets in which tokens are equipped with attributes (or colors). Figure 6 shows an OrchNet equipped with attributes The presence of dates in tokens alters the firing semantics slightly. A transition t is enabled at date when all places in its preset have tokens. It then takes τ t additional time to fire. For example, the shaded transition in the left has all its input tokens at max{d 2 , d 0 + τ m } and so it fires at max{d 2 , d 0 + τ m } + 0 since it has zero latency. If a transition fires at date d, then the tokens in its postset have the date d. This is shown in the figure, e.g., on the place following the left shaded transition, which has date max{d 2 , d 0 + τ m }.

m n t d1 d2 τn τ = 0 τt τs τ = 0 τm d0 + τm d1 + τn d ′ = max{d2, d1 + τn} d0 E =    case d < d ′ then d + τs case d > d ′ then d ′ + τt otherwise nondeterministic d = max{d2, d0 + τm} s .
When transitions are in conflict, (e.g., the two shaded transitions in Figure 6), the transition that actually occurs is governed by a race policy [START_REF] Marco Ajmone Marsan | Modelling with generalized stochastic petri nets[END_REF]. If a set of enabled transitions are in conflict, the one with smallest date of occurrence will fire, preempting the other transitions in conflict with it. So, in Figure 6, the left shaded transition or the right shaded transition will fire depending on whether d < d ′ or d > d ′ respectively, with a nondeterministic choice if d = d ′ . This results in selecting the left most or right most continuation (firing s or t) depending on the above cases. The resulting overall latency E of the orchestration is shown at the bottom of the figure.

In addition to dates, tokens in OrchNets can have data attributes, which we call values. We have not shown this in Figure 6, in order to keep it simple. Values of tokens in the preset of a transition t can be combined by a value function φ t attached to t. The resulting value is taken by the token in the postset of t.

Transitions can also have guards (the presence of such a guard is not necessary). Guards are boolean predicates involving values of the tokens in the transition's preset. A transition is enabled only if its guard is true. An "If(cond)then-else" branching can be implemented by using the following mechanism: Put a place p, followed by two transitions t, t ′ . Guard t with the predicate "cond=true" and t ′ with the predicate "cond=false".

At this point we are ready to provide the formal definition of OrchNets:

Definition 6 (OrchNet) An OrchNet is a tuple N = (N, Φ, T, T init ) consist- ing of
An occurrence net N with token attributes c = (value, date).

A family Φ = (φ t ) t∈T of value functions, whose input parameters are the values of the transition's input tokens.

A family T = (τ t ) t∈T of latency functions, whose input parameters are the values of the transition's input tokens. The range of the latency functions is in R ∪ {+∞} A family T init = (τ p ) p∈min(P) of initial date functions for the minimal places of N . The range of the initial date functions is in R ∪ {+∞}

We do not specify a concrete range of value functions since they can be any arbitrary value and this is not of direct importance in the sequel. How a transition t modifies the attributes of tokens is formalized now: Let the preset of Then all the tokens in the postset of t have the pair (v t , d t ) of value and date, where:

v t = φ t (v 1 . . . v n ) d t = max{d 1 . . . d n } + τ t (v 1 . . . v n ) (1)
The race policy during execution is formalized as follows: In any given marking M , let T be the set of transitions that are possibly enabled, i.e. ∀t ∈ T , • t is marked in M . Then the transition t that is actually enabled, (which really fires) is given by: t = arg min

t∈T d t
where arg min f (x

) x∈X = x * ∈ X s.t. ∀x ′ ∈ X, f (x * ) ≤ f (x ′ ).
If two transitions have the same d t , then the choice of the transition that actually fires is non-deterministic. If for a transition t, the delay d t is infinite, it is equivalent to saying that transition t does not occur.

The choice extensions to occurrence nets in OrchNets is inspired by the application domain: compositions of web services. It reflects the following facts.

Since we focus on latency, (value, date) is the only needed color.

Orchestrations rarely involve decisions on actions based on absolute dates. Timeouts are an exception, but these can be modelled explicitly, without using dates in guards of transitions. This justifies the fact that guards only have token values as inputs, and not their dates.

The time needed to perform transitions does not depend on the tuple of dates (d 1 . . . d n ) when input tokens were created, but it can depend on the data (v 1 . . . v n ) and computation φ performed on these. This justifies our restriction for output arc expressions.

If it is still wished that control explicitly depends on dates, then dates must be measured and can then be stored as part of the value v.

Actually Occurring Configuration and Execution Time In general, both value and latency functions can be nondeterministic. We introduce an invisible daemon variable ω that resolves this nondeterminism and we denote by Ω its domain. For a given value of ω, the value and latency functions φ ω t and τ ω t are deterministic functions.

Let N = (N, Φ, T, T init ) be a finite OrchNet. For a value ω ∈ Ω for the daemon we can calculate the following dates for every transition t and place p of N :

d p (ω) = τ ω p if p is minimal d s (ω) where s = • p otherwise d t (ω) = max{d n (ω) | n ∈ • t} + τ ω t (v 1 , . . . v n ) (2)
where v 1 , . . . v n are the value components of the tokens in • t as in equation ( 1). If κ is a configuration of N , the future N κ is the OrchNet (N κ , Φ N κ , T N κ , T ′ init ) where Φ N κ and T N κ are the restrictions of Φ and T respectively, to the transitions of N κ . T ′ init is the family derived from N according to (2): for any minimal place p of N κ , the initialisation function is given by τ ′ p ω = d p (ω). For X a set of nodes of N , let

T min (X) = {t ∈ T (X) | •• t ∩ X = ∅} Now define inductively, κ 0 (ω) = ∅ κ m (ω) = κ m-1 (ω) ∪ {t m } ∪ • t m ∪ t m • (3) where t m = arg min t∈Tmin(N κ m-1 (ω) ) d t (ω)
Since net N is finite, the above inductive definition terminates in finitely many steps when N κm(ω) = ∅. Let M (ω) be this number of steps. We thus have

∅ = κ 0 ⊂ κ 1 (ω) • • • ⊂ κ M(ω) (ω)
κ M(ω) (ω) is a maximal configuration which actually occurs according to our timed semantics, for a fixed ω. Each step decreases the number of maximal configurations sharing κ m (ω) as a prefix. We denote by κ(N , ω), the maximal configuration κ M(ω) (ω) that actually occurs. For a prefix B of N define

E ω (B, N ) = max{d x (ω) | x ∈ B} (4)
If B is a configuration, then E ω (B, N ) is the time taken for B to execute (latency of B). The latency of the OrchNet N = (N, Φ, T, T init ), for a given ω is

E ω (N ) = E ω (κ(N , ω), N )

Characterizing monotony

In this article, we are interested in the total time taken to execute a webservice orchestration. As a consequence, we will consider only orchestrations that terminate in a finite time, i.e, only a finite number of values can be returned.

Defining monotony

To formalize monotony we must specify how latencies and initial dates can vary. As an example, we may want to constrain some pair of transitions to have identical latencies, or some pair of minimal places to have identical initial dates. This allowed flexibility in setting latencies or initial dates is formalized under the notion of pre-OrchNet we introduce next.

Definition 7 (pre-OrchNet) Call pre-OrchNet a tuple N = (N, Φ, T, T init ), where N and Φ are as before, and T and T init are sets of families T of latency functions and of families T init of initial date functions. Write N ∈ N if N = (N, Φ, T, T init ) for some T ∈ T and T init ∈ T init .

For two families T and T ′ of latency functions, write

T ≥ T ′

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to mean that ∀ω ∈ Ω, ∀t ∈ T =⇒ τ t (ω) ≥ τ ′ t (ω), and similarly for

T init ≥ T ′ init . For N , N ′ ∈ N, write N ≥ N ′ if T ≥ T ′ and T init ≥ T ′ init both hold. Definition 8 (monotony) pre-OrchNet N = (N, Φ, T, T init ) is called mono- tonic if, for any two N , N ′ ∈ N, such that N ≥ N ′ , we have E ω (N ) ≥ E ω (N ′ ).
Considering legal sets T and T init of families of latency functions and initial date functions allows setting constraints on these families. This possibility will be essential in characterizing monotonic orchestrations.

A global necessary and sufficient condition

Theorem 1

1. The following condition implies the monotony of pre-OrchNet N = (N, Φ, T, T init ):

∀N ∈ N, ∀ω ∈ Ω, ∀κ ∈ V (N ) , E ω (κ, N ) ≥ E ω (κ(N , ω), N ) (5)
where V (N ) denotes the set of all maximal configurations of net N and κ(N , ω) is the maximal configuration of N that actually occurs under the daemon value ω.

Conversely, assume that:

(a) Condition ( 5) is violated, and (b) for any two OrchNets N and N ′ such that N ∈ N, then N ′ ≥ N =⇒ N ′ ∈ N.

Then N = (N, Φ, T, T init ) is not monotonic.

Sub-condition b) in statement 2 destroys the necessity of Condition [START_REF] Kitchin | A language for task orchestration and its semantic properties[END_REF]. Statement 2 expresses that Condition ( 5) is also necessary provided that it is legal to increase at will latencies or initial dates. Observe that Condition (5) by itself cannot be enough since it trivially holds if T is a singleton.

Proof: We first prove Statement 1. Let N ′ ∈ N be such that N ′ ≥ N . We have:

E ω (κ(N ′ , ω), N ′ ) ≥ E ω (κ(N ′ , ω), N ) ≥ E ω (κ(N , ω), N )
where the first inequality follows from the fact that κ(N ′ , ω) is a conflict free partial order and N ′ ≥ N , and the second inequality follows from (5) applied with κ = κ(N ′ , ω). This proves Statement 1. We prove statement 2 by contradiction. Let (N , ω, κ † ) be a triple violating Condition [START_REF] Kitchin | A language for task orchestration and its semantic properties[END_REF], in that

κ † cannot occur (6) E ω (κ † , N ) < E ω (κ(N , ω), N ) (7)
Now consider the OrchNet net N ′ = (N, Φ, T ′ , T init ) where the family T ′ is the same as T except that in ω, ∀t / ∈ κ † , τ ′ t (ω) > E ω (κ † , N ). Clearly N ′ ≥ N . But using construction (3), it is easy to verify that κ(N ′ , ω) = κ † and thus

E ω (κ(N ′ , ω), N ′ ) = E ω (κ † , N ′ ) = E ω (κ † , N ) < E ω (κ(N , ω), N ),
which violates monotony. ⋄

A structural condition for the monotony of workflow nets

Workflow nets [START_REF] Wil | Verification of workflow nets[END_REF] were proposed as a simple model for workflows. These are Petri nets, with a special minimal place i and a special maximal place o. We consider the class of workflow nets that are 1-safe and which have no loops. Further, we require them to be sound [START_REF] Wil | Verification of workflow nets[END_REF].

Definition 9 A Workflow net W is said to be sound iff:

1. For every marking M reachable from the initial place i, there is a firing sequence leading to the final place o.

2. If a marking M marks the final place o, then no other place can in W can be marked in M 3. There are no dead transitions in W . Starting from the initial place, it is always possible to fire any transition of W .

An example of workflow net is shown in the first net of Figure 4. Workflow nets will be generically denoted by W . We can equip workflow nets with same attributes as occurrence nets, this yields pre-WFnets W = (W, Φ, T, T init ). Referring to the end of Section 3.1, unfolding W yields an occurrence net that we denote by N W with associated morphism ϕ W : N W → W , see Figure 4. Here the morphism ϕ W maps the two c transitions (and the place in its preset and postset) in the net on the right to the single c transition (and its preset and postset) in the net on the left. Observe that W and N W possess identical sets of minimal places. Morphism ϕ W induces a pre-OrchNet

N W = (N W , Φ W , T W , T init )
by attaching to each transition t of N W the value and latency functions attached to ϕ W (t) in W.

We shall use the results of the previous section in order to characterize those pre-WFnets whose unfoldings give monotonic pre-OrchNets. Our characterization will be essentially structural in that it does not involve any constraint on latency functions beyond equality constraints, for some pairs of transitions. Under this restricted discipline, the simple structural conditions we shall formulate will also be almost necessary.

We first define a notion of cluster on safe nets, which will be useful for our characterisation.

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Definition 10 (clusters) For a safe net N , a cluster is a minimal set c of places and transitions of N such that

∀t ∈ c =⇒ • t ⊆ c , ∀p ∈ c =⇒ p • ⊆ c (8)
Theorem 2 (Sufficient Condition) Let W be a WFnet and N W be its unfolding. A sufficient condition for the pre-OrchNet

N W = (N W , Φ W , T W , T init )
to be monotonic is that every cluster c satisfies the following condition:

∀t 1 , t 2 ∈ c, t 1 = t 2 =⇒ t 1 • = t 2 • (9)
Proof: Let ϕ W be the net morphism mapping N W onto W and let N ∈ N be any OrchNet. We prove that condition 1 of Theorem 1 holds for N by induction on the number of transitions in the maximal configuration κ(N , ω) that actually occurs. The base case is when it has only one transition. Clearly this transition has the least latency and any other maximal configuration has a greater execution time.

Induction Hypothesis Condition 1 of Theorem 1 holds for any maximal occurring configuration with m -1 transitions (m > 1). Formally, for a pre-

OrchNet N = (N, Φ, T, T init ): ∀N ∈ N, ∀ω ∈ Ω, ∀κ ∈ V (N ), E ω (κ, N ) ≥ E ω (κ(N , ω), N ) (10)
holds if |{t ∈ κ(N , ω)}| ≤ m -1.
Induction Argument Consider the OrchNet N , where the actually occurring configuration κ(N , ω) has m transitions. κ ′ is any other maximal configuration of N . If the transition t in κ(N , ω) with minimal date d t also occurs in κ ′ then comparing execution times of κ(N , ω) and κ ′ reduces to comparing E ω (κ(N , ω)\ {t}, N t ) and E ω (κ ′ \ {t}, N t ). Since κ(N , ω) \ {t} is the actually occurring configuration in the future N t of transition t, using our induction hypothesis, we have

E ω (κ(N , ω) \ {t}, N t ) ≤ E ω (κ ′ \ {t}, N t )
and so

E ω (κ(N , ω), N ) ≤ E ω (κ ′ , N )
If t / ∈ κ ′ for some κ ′ , then there must exist another transition t ′ such that • t ∩ • t ′ = ∅. By the definition of clusters, ϕ W (t) and ϕ W (t ′ ) must belong to the same cluster c. Hence, t • = t ′ • follows from condition 9 of Theorem 2. The futures N t and N t ′ thus have identical sets of transitions: they only differ in the initial marking of their places. If T init and T ′ init are the initial marking of these places,

T init ≤ T ′ init (since d t ≤ d t ′ , t • has dates lesser than t ′ • ). Hence E ω (κ(N , ω), N ) = E ω (κ(N , ω) \ {t}, N t ) (11)
and

E ω (κ ′ , N ) = E ω (κ ′ \ {t ′ }, N t ′ ) ≥ E ω (κ ′ \ {t ′ }, N t ) (12)
The inequality holds since N t ′ ≥ N t . The induction hypothesis on [START_REF] Wil | Verification of workflow nets[END_REF] and ( 12) gives

E ω (κ(N , ω), N ) ≤ E ω (κ ′ , N )
This proves the theorem. ⋄

Comments about tightness of the conditions of Theorem 2 Recall that the sufficient condition for monotony stated in Theorem 1 is "almost necessary" in that, if enough flexibility exist in setting latencies and initial dates, then it is actually necessary. It turns out that the same holds for the sufficient condition stated in Theorem 2 if the workflow net is assumed to be live.

Theorem 3 (Necessary Condition) Suppose that the workflow net W is sound. Assume that W ∈ W and W ′ ≥ W implies W ′ ∈ W, meaning that there is enough flexibility in setting latencies and initial dates. In addition, assume that there is atleast one W * ∈ W such that there is an daemon value ω * for which the latencies of all the transitions are finite. Then the sufficient condition of Theorem 2 is also necessary for monotony.

Proof: We will show that when condition (9) of Theorem 2 is not satisfied by W , the Orchnets in its induced preOrchNet N W can violate condition (5) of Theorem 1, the necessary condition for monotony. Let c W be any cluster in W that violates the condition 9 of Theorem 2. Consider the unfolding of W , N W and the associated morphism ϕ : N W → W as introduced before. Since W is sound, all transitions in c W are reachable from the initial place i and so there is a cluster c in N W such that ϕ(c) = c W . There are transitions t 1 , t 2 ∈ c such that

• t 1 ∩ • t 2 = ∅, • ϕ(t 1 ) ∩ • ϕ(t 2 ) = ∅ and ϕ(t 1 ) • = ϕ(t 2 ) • . Call [t] = ⌈t⌉ \ {t} and define K = [t 1 ] ∪ [t 2 ]
. We consider the following two cases: K is a configuration If so, consider the OrchNet N * ∈ N W got when transitions of N W (and so W ) have latencies as that in W * . So for the daemon value ω * , the quantity E ω * (K, N * ) is some finite value n * . Now, configuration K can actually occur in a OrchNet N , such that N > N * , where N is obtained as follows (τ and τ * denote the latencies of transitions in N and N * respectively):

∀t ∈ K, t ′ ∈ N W s.t. • t ∩ • t ′ = ∅, set τ t ′ (ω * ) = n * + 1
and keep the other latencies unchanged. In this case, for the daemon value ω * , the latencies of all transitions of N (and so its overall execution time) is finite. Denote by N K the future of N once configuration K has actually occurred. Both t 1 and t 2 are minimal and enabled in N K .

Since ϕ(t 1 )

• = ϕ(t 2 )

• , without loss of generality, we assume that there is a place p ∈ t 1

• such that ϕ(p) ∈ ϕ(t 1 )

• but ϕ(p) / ∈ ϕ(t 2 )

• . Let t * be a transition in N K such that t * ∈ p • . Such a transition must exist since p can not be a maximal place: ϕ(p) can not be a maximal place in W which has a unique maximal place. Now consider the Orchnet N ′ > N got as follows:

τ ′ t1 (ω * ) = τ t1 (ω * ), τ ′ t2 (ω * ) = τ t1 (ω * ) + 1 and for all other t ∈ c, τ ′ t (ω * ) = τ ′ t2 (ω * ) + 1. Set τ ′ t * (ω * ) =
∞ and for all other transitions of N ′ , the delays are the same as that in N and thus are finite for ω * .

INRIA t 1 has the minimal delay among all transitions in c, and t * is in the future of t 1 . So the actually occuring configuration E ω * (κ(N ′ , ω * ), N ′ ) has an infinite delay. However any maximal configuration κ which does not include t 1 (for eg, when t 2 fires instead of t 1 ) will have a finite delay. For such κ we thus have E ω * (κ(N ′ , ω * ), N ′ ) > E ω * (κ, N ′ ) and so N ′ violates the condition (5) of Theorem 1.

K is not a configuration If so, there exist transitions t

∈ [t 1 ] \ [t 2 ], t ′ ∈ [t 2 ] \ [t 1 ] such that • t ∩ • t ′ = ∅, • ϕ(t) ∩ • ϕ(t ′ ) = ∅ and ϕ(t) • = ϕ(t ′ )
• . The final condition holds since t 2 and t 1 are not in the causal future of t and t ′ respectively. Thus t and t ′ belong to the same cluster, which violates condition 9 of Theorem 2 and we can apply the same reasoning as in the beginning of the proof. Since [t] is finite for any transition t, we will eventually end up with K being a configuration. ⋄

Discussion regarding monotony

Based on the mathematical results of the former section, we shall first discuss which orchestrations are monotonic. The resulting class is not very wide, as we shall see. However, further thinking suggests that considering QoS parameters in isolation -as we did so far -is not the right way to proceed. We will thus revisit QoS and monotony.

Which orchestrations are monotonic? Not surprisingly, orchestrations involving no choice at all -they are modeled by event graphs -are monotonic.

Theorem 2, however, allows for more general orchestrations. In particular, if multi-threading with only conflicting threads are used, then the theorem essentially requires that the choice among the different threads is performed, based on their overall latency (where a thread is considered as atomic). It is allowed, however, that conflicting threads possess different overall latencies. Next, if a blend of concurrent and conflicting multi-threading is used, then 1/ concurrent threads should have equal latencies, and 2/ the choice among conflicting threads should be based on their overall latency. Finally, concurrent multi-threading (with no conflict with other thread when the concurrent threads are launched) raises no problem. An example of a non trivial monotonic orchestration is shown in Figure 4.

Revisiting QoS and monotony As discussed before, orchestrations involving data dependent control will very often be non monotonic. This makes SLA/SLS/contract based QoS management very problematic. What did we wrong?

In fact, the problem is that we consider QoS parameters in isolation when dealing with SLS or contracts. However one can trade latency for "quality of data". Typically, by reducing timeouts while waiting for responses from called Web services, one can easily reduce latency. But there is no free lunch: if one does so, then exceptions get raised in lieu of getting valid responses for the query.

So we must refine our notion of monotony as follows: say that an orchestration is "conditionally monotonic" if, under the constraint that identical responses are received by the orchestration, increasing some latency will cause an increase of the overall latency of the orchestration. In the next section we formalize this notion and study the characterization of conditional monotony.

Refined QoS and Conditional monotony

Define the set of values returned by a maximal configuration κ ∈ V (N ) as

V ω (κ, N ) = {φ t (ω) | t ∈ max(κ)}
where max(κ) denotes the maximal (w.r.t ≤) transitions in the configuration κ. The values returned by the orchestration N = (N, φ, T, T init ) for a given value of the daemon ω is

V ω (N ) = V ω (κ(N , ω), N ) Definition 11 (conditional monotony) pre-OrchNet N = (N, Φ, T, T init ) is called conditionally monotonic if, ∀N , N ′ ∈ N s. t. N ≥ N ′ and ∀ω ∈ Ω s. t. V ω (N ) = V ω (N ′ ) ⇒ E ω (N ) ≥ E ω (N ′ )
Definition 11 does not attempt to compare overall orchestration latencies, if different responses are received as a result of changing latencies of called Web services. In particular, cases where valid data are received are not compared with cases where exceptions are raised. Said differently, Definition 11 prohibits trading latency for quality of data. Conditional monotony does not seem to be considered while formulating WSLA contracts. The 'conditional' contracts in WSLA are not related to the notion of conditional monotony but rather refer to the obligations that need to be met by the client for the server's promises to be fulfilled.

Assumption 1 We assume that OrchNet N is such that for all distinct κ, κ ′ ∈ V (N ), V ω (κ, N ) = V ω (κ ′ , N ). Assumption 1 is very natural when normal processing of the orchestration together with cases where exceptions occur are considered. With this assumption, Theorem 1 simplifies as follows:

Theorem 4 Under Assumption 1 pre-OrchNet N = (N, Φ, T, T init ) is conditionally monotonic.

Proof: In fact this is a trivial result: by Assumption 1, we do not need to compare latencies across different configurations. But each configuration possesses no conflict and is therefore an event graph. Since dating in event graphs is amenable of max /+ algebra, it is monotonic. Thus pre-OrchNet N = (N, Φ, T, T init ) is conditionally monotonic. ⋄

INRIA 6 Conclusion

This paper is a contribution to the fundamentals of contract based QoS management of Web services orchestrations/choreographies. QoS contracts implicitly assume monotony w.r.t. QoS parameters. This paper focuses on one specific (but representative) QoS parameter, namely latency or response time. We have shown that monotony is very easily violated in realistic cases. We have formalized monotony and have provided necessary and sufficient conditions for it. As we have seen, QoS can be very often traded for Quality of Data: poor quality responses to queries (including exceptions or invalid responses) can be obtained typically much faster. This reveals that QoS parameters should not be considered separately, in isolation. We have thus revisited the notions of latency and monotony and proposed the new concept of conditional monotony. Fortunately enough, typical orchestrations turn out to be non-monotonic, but conditionally monotonic.

Our study has an impact on the way SLS should be phrased for orchestrations: it suggests crude contracts such as "for 95% of the requests the response time will be less than 5ms" should not be used without referring to the quality of data. Also, our study has an impact on contract monitoring -monitoring whether a called service meets its contract.

We see two extensions of this work. First, our mathematical results rely on the notion of branching cells, which were developed for nets without read arcs. However, advanced orchestration languages such as Orc [START_REF] Misra | Computation orchestration: A basis for wide-area computing[END_REF] offer a sophisticated form of preemption that requires contextual nets (with read arcs) for their modeling. Extending our results to this case is non trivial since branching cells do not exist for contextual nets. Second, this paper considers latencies in a non probabilistic context. However, these authors advocated in [START_REF] Rosario | Probabilistic QoS and soft contracts for transaction based web services[END_REF] the use of probabilistic contracts -they better reflect the uncertain nature of QoS parameters in the open world of the Web and they allow for well sound overbooking and less pessimistic contracts. We should extend our present work to this probabilistic framework. This should not be too difficult, as we guess. In fact, a theory of monotony for probabilistic QoS must rely on an order among probability distributions. This exists and is known as stochastic ordering. Results are available that relate stochastic ordering and point-wise ordering (as we study here), which should be of help for such an extension.

  with four transitions a, b, c and d with latencies τ a , τ b , τ c and τ d respectively. Let τ a = 2, τ b = 3, τ c = 4 and τ d = 7. Here a fires before b and the overall orchestration latency is τ a + τ c = 6. Now, if τ b = 1, b fires before a and so the orchestration latency is τ b + τ d = 8. Since decreasing the latency of b increases the orchestration's latency, the net is not monotonic. Non-monotony arises from the fact that the futures of the conflicting transitions a and b had different latencies. The net is monotonic if the latencies of c and d are constrained to be the same.

Figure 2 :

 2 Figure 2: Choices are not monotonic.

RR n 6528 In Figure 3 ,

 65283 transitions a and c are concurrent, a#b and b#c. Since we saw in the previous example that the futures of conflicting transitions should have the same latencies, let us set τ d = τ e = τ f = τ * . If τ a = 4, τ b = 3, τ c = 5, b fires first and the overall latency is τ b + τ e = 4 + τ * . Now if τ a = 2, a fires first, b is blocked and c will eventually fire.

Figure 2 .

 2

Figure 3 :

 3 Figure 3: Choice and Concurrency inter-playing

Figure 4 :

 4 Figure 4: A monotonic orchestration with a fork-join pattern (left) and its unfolding (right).

INRIA

1 Figure 5 :

 15 Figure 5: Construction of the unfolding U N of a safe net N .

Figure 6 :

 6 Figure 6: A Generic Transition of our Model. The arc expressions are shown next to the arcs and the guard expression is written next to the transition.

INRIAt

  have n places whose tokens have (value, date) attributes (v 1 , d 1 ) . . . (v n , d n ).

RR n 6528

* This work was partially funded by the ANR national research program DOTS (ANR-06-SETI-003), DocFlow (ANR-06-MDCA-005) and the project CREATE ActivDoc.