Guillaume Jacques

Evangelia Adamou

Denis Creissels

Bernd Heine

Nathan W Hill

Katarzyna Janic

Aimée Lahaussois

Sergey Say

Denominal affixes as sources of antipassive markers in Japhug Rgyalrong *

Keywords: Antipassive, applicative, causative, denominal verbs, nominalization, action nominalls, Rgyalrong, Japhug, Nahuatl, Eskaleut, Grammaticalization

In this paper, we review the documented diachronic pathways leading to antipassive markers in the world's languages and show that Japhug Rgyalrong, a polysynthetic language belonging to the Sino-Tibetan family, attests a previously unreported source of antipassives.

In Japhug, the two antipassive constructions (human and non-human antipassive) are built from the base verb through a two-step process: first nominalization into an action nominal, and second denominal verbalizing derivation of the action noun into an intransitive verb. Nominalization neutralizes the verb's transitivity, and a new transitivity value is allocated by the denominal prefix.

A similar pathway is proposed for other derivations, in particular the applicative.

Introduction

The diachronic origin of antipassive markers, unlike that of passive markers and constructions (for instance Haspelmath 1990), has only attracted a limited amount of scholarship. 1 This lack of research is due in part to the fact that antipassive constructions are less common than passive ones cross-linguistically, but also that many constructions that could have been 1 described as antipassives are usually described with a different terminology, especially in languages whose flagging is aligned accusatively.

Antipassives are overtly marked intransitivizing constructions that demote the patient of transitive verbs, whereby the agent of the original verb (A) becomes the only argument (S) of the verb in the antipassive construction; the demoted O either receives oblique case or is deleted from the construction. This definition allows for constructions variously labelled as 'depatientive', 'detransitive', 'deaccusative' or 'deobjective' in accusative languages2 to be designated as antipassive, following authors such as Heath 1976, Polinsky (2011) and Creissels (2012), but excludes agent-preserving lability and incorporation.

Previous work has pointed out five cross-linguistic origins for antipassive markers, presented in the following table : 3 Eskaleut Fortescue (1996) The first three origins can involve the intermediate stage of a middle construction. Nominal origins (such as body) are well-attested for reflexive, reciprocal and middle markers (Heine and Kuteva 2002: 58), but no such case has been reported for antipassive constructions.

The last pathway, namely derivation from antipassive periphrases with the verb 'make' or 'get', has only been described for two groups of languages: Eskaleut and Mande.

In West Greenlandic, we find three antipassive ('half-transitive') suffixes: -(s)i-, -nnigand -ller-. 4 According to Fortescue (1996), all three suffixes originate from the combination of nominalizing or participial suffixes with a postbase (bound stem):

• -(s)iresults from the fusion of the passive participle *-aR with the postbase *-li 'to make, to become' (Fortescue et al. 2010: 438, 447).

The change of proto-Eskimo * -to Greenlandic sis regular.

• -nnigcomes from the fusion of the nominalizer *-n R with the verb *-n ɣ 'to get' (Fortescue et al. 2010: 457, 459).

• -lleroriginates from a nominalizer (which could be either the nominalizer *-or the passive participle *-ka -) combined with the postbase *-l ɣ 'to provide with' (Fortescue et al. (2010: 451, 442, 459))

In West Mande, Creissels (2012) similarly argues that the antipassive suffixes -ndi ̀in Soninke originate from a verb root that can be reconstructed as *tin 'to do', and that the antipassive construction in question comes from a periphrase comparable to French acheter ('to buy', transitive) ⇒ faire des achats ('to do shopping', with the verb faire 'to do').

In this paper, we present a related, but slightly different, pathway of grammaticalization of the antipassive in Japhug, a polysynthetic Sino-Tibetan language spoken in Sichuan, China. Like the Greenlandic case, it involves two steps: nominalization of a transitive verb and then denominal derivation back into a verb. An important difference of the Japhug case from both Eskaleut and West Mande is that denominal derivational prefixes cannot be etymologically derived from a verb. 5 This paper is divided into four sections. First, we present background information on Japhug in general, in particular on nominalization and transitivity. Second, we offer an account of the antipassive construction in Japhug and discuss all the derivational prefixes homophonous with the antipassive prefixes. Third, we provide arguments showing that one of the two antipassive prefixes originates from a denominal construction. Fourth, we show that a similar scenario can be proposed to explain the origin of the applicative marker.

Background information

Japhug Rgyalrong is a polysynthetic language belonging to the Sino-Tibetan family, spoken by fewer than 10000 speakers in Mbarkhams county, Rngaba district, Western Sichuan, China.

The closest relatives of Japhug are the other Rgyalrong languages: Situ, Tshobdun, and Showu. The distribution of the four Rgyalrong languages is indicated in Figure 1; the black dot represents the Japhug speaking area.

Like other Rgyalrong languages, Japhug presents a very rich system of prefixal voice derivation, including causative, applicative, passive, anticausative, antipassive (Jacques 2012b) and incorporation (Jacques 2012c); transitive verbs agree with two arguments in person and number. In this section, we present all background information needed to follow the argumentation: transitivity marking in Japhug, nominal morphology and nominalization. Antipassive derivation in Japhug is described in more detail in section 3. We will in particular discuss the fact that no less than four different tprefixes are found in nouns, a topic that will be of importance for our diachronic hypothesis in section 4.

Nominal morphology

As the present article will discuss the derivation of verbs from nouns, some information on nominal morphology is necessary. Three features of nouns are described here: possession and number.

The main morphological feature of Japhug nouns is possession. Nouns can be divided into two main categories: inalienably and alienably possessed nouns. 6 Inalienably possessed nouns require a possessive prefix in all cases, while alienably possessed nouns may or may not have such a prefix.

Inalienably possessed nouns must either bear one of the possessive prefixes in Table 2. The indefinite possessive prefix has two variants t -and t -whose distribution is lexically determined. Alienably possessed nouns can take the prefixes in Table 2, but not the indefinite possessive prefix. In this paper, inalienably possessed nouns will be cited by their root form with a hyphen indicating the obligatory presence of a possessive prefix. Thus -ja 'hand' implies that the form *ja on its own is not possible for the meaning 'hand', and one will either find the indefinite form t -ja 'someone's hand' or a form with a possessive prefix such as a-ja 'my hand', n -ja 'your hand' etc.

Inalienably possessed nouns (1 and 2) can be converted to alienably possessed by adding a possessive prefix before the indefinite possessor (example 3).

(1) -r 3sg.poss-horn

Its horn

(2) ta-r indef.poss-horn A horn

(3) -ta-r 3sg.poss-indef.poss-horn His horn (the horn taken from an animal) This phenomenon is not restricted to Rgyalrong languages, but also found in other languages with possessive affixes, such as Athabaskan. 7 Aside from possessive prefixes, an important morphological category occurring in the nominal domain are the numeral prefixes of quantifier nouns (Table 3; only numerals up to 10 are indicated, but all numerals up to one hundred can occur as prefixes). These nouns include measure of time (t -xpa 'one year' etc), of length (t -tɣa 'one handspan' etc), various quantities (t -ɣd t 'one section' etc) or classifiers (t -rdo 'one piece' etc).

Table 3: Numerals and numeral prefixes in Japhug

Numeral prefix

1 ci t - 2 n z n - 3 s m s - 4 k de k de- 5 k m u k m u- 6 k t ɣ-k t - 7 k ɕn z k ɕn - 8 k rcat k rc - 9 k ng t k ng - 10 sqi sq -
Although the numeral prefix tis formally similar to the indefinite possessor t -, the two are entirely distinct, as they alternate within different paradigms (respectively Tables 2 and3). It is not possible to add both series of prefixes on the same quantifier noun. Non-quantifier nouns cannot receive numeral prefixes.

Numeral prefixes are obligatory with quantifier nouns. The only exception is observed with measures of time: the numeral prefixes can be replaced with the third person possessiveto express the meaning 'that (particular) year', 'that day' etc, as in example 4. No other possessive prefix may be used with these measure nouns.

flesh' and she-'a-ts ' 1sg.poss-indef.poss-flesh. 'my meat (bought at the marker)' (Young and Morgan 1987: 10). The theoretical implications of this phenomenon go beyond this paper.

Nominalization

Japhug Rgyalrong, like other Rgyalrong languages (see for instance Sun 2003 on the Tshobdun language), has a very rich system of nominalization prefixes. Four different prefixes are productive: the S/A nominalization k -, the O nominalization k -, the oblique nominalization sand the action nominalization t -. This section will briefly describe the first three, then describe the prefix t -and prefixless nominalized forms in more detail, as the latter two will be more relevant to our diachronic hypothesis in section 4.

Argument and adjunct nominals

The nominalized forms derived with the three first prefixes k -, k -and s -are fully productive, and can be used to build relative clauses (Jacques 2004: 464-9). The S/A nominalization prefix kappears with both intransitive and transitive verbs, but in the latter case a possessive prefix (from Table 2) coreferent with the patient is added (see 6). This nominalized form can be used as one of the tests to determine whether a particular verb is transitive or intransitive (cf section 2.3)

(5) k -si nmlz:S/A-die 'The dead one'.

(6) -k -sat 3sg-nmlz:S/A-kill 'The one who kills him.'

The nominalization prefix k -has two irregular forms ɣor xwhich can be found in a few nouns (Table 4). Most of these nouns are possessed nouns, but mainly occur with the third person singular possessive -. The semantic relationship between the base verb and the derived nouns in Table 4 is not entirely obvious synchronically, as the nouns have undergone an independent semantic evolution. The changes from /k/ → /ɣ/ and /k/ → /x/ on the other hand are perfectly regular in Japhug; the phonological irregularity lies in the loss of the vowel only.

As the first element of a cluster in Japhug, stops only occur before the non-nasal sonorants /r/, /j/, /w/, /l/ and /ɣ/. 8 This gap in the distribution of velar and labial is accounted for if we take into consideration the fact that clusters with velar or labial fricatives as their first element in Japhug always correspond to clusters with velar or labial stops in the closely related Situ language (Jacques 2004: 270; for instance, -xt ɣ 'brother' corresponds to Situ Rgyalrong -kteḱ), which suggests that as the first element of clusters, stops have undergone fricativisation in Japhug.

Since the language disallows clusters of the type stop+nasal as well as stop+s altogether, and since the velar fricatives /x/ and /ɣ/ always agree in voicing with the following consonant in clusters (all other possibilities -*kn-, *xn-, *gn-, are not acceptable clusters in Japhug). Note that irregular nouns in Table 4 are attested for only verbal roots with a simple initial consonant, without any cluster (prenasalized voiced obstruents count as one phoneme in Japhug). This is by no means a coincidence, but rather an effect of the fact that with clusters, the /k-/ prefix would have been dropped without a trace.

Alongside the nouns in table 4, all four verbs allow the phonologically and semantically regular corresponding nominalized forms (k -a 'the black one', k -so 'the empty one' etc), which were regularly created after the irregular nominalizations became opaque.

The irregular loss of vowels in the examples in table 4 is by no means limited to the nominalization prefix k -, as it is also observed with the animal class prefixes k -which becomes x-/ɣin some examples but not in others. Comparison with Situ Rgyalrong, which never undergoes vowel loss in prefixes, allows one to detect these examples. Vowel attrition of prefixes occurs either with non-productive prefixes such as the animal class prefix or with productive prefixes (such as the S/ A nominalization prefix k -) that become reanalysed as a part of the stem due to the semantic evolution of the deverbal noun in question. Another such example is studied in section 2.2.2.

Action nominals

Beside the argument and adjunct nominalization prefixes studied in the previous subsection, we also find action or result nominals in t -.

The literature on Rgyalrong languages designates these forms as 'action nouns' (Jacques 2004: 455) or 'lexicalized action nominals' (Sun and Lin 2007). 10 Action nominals can be used to refer to the action or process designated by the verb. They can occur in constructions with a light verb such as (7), or as the complement of the verb ʑa 'to begin' ( 8 Action nominals cannot take any TAM markers but can receive possessive prefixes. However, the possessor does not necessarily correspond to any of the arguments of the original verb. For instance, in the case of the noun t -r a 'a dance' derived from the intransitive r a 'to dance', possessive prefixes as in -t -r a 'his dance' are generally interpreted as the beneficiary of the action, not the dancer ('a dance performed in his honour').

With stative verbs, t -nominals express the abstract property of the verb (like the derivation of nouns from adjectives by the suffix -ness in English) and are better labelled as 'property nominals'. t -nominals commonly occur in a degree construction, followed by another stative verb indicating degree such as sa a 'to be extremely ...' or s re 'to be ridiculous, to be terribly . Unlike the argument nominals discussed in the previous subsection, taction nominal derivation is not fully productive, and the semantics of the action nominals is not always predictable. In some cases, it refers to the result of the action rather than the action itself (thus t -ta 'woven cloth' from ta 'to weave') or even the object of the action (t -ts i 'rice porridge' from ts i 'to drink') and the semantics of the noun is not always predictable and tends to be more specific than that of the verb. It is however crosslinguistically quite common for action nominals to present this kind of irregular semantics for some nouns (Koptjevskaja-Tamm 1993: 20-21). In the following, we provide a detailed account of one action nominal with irregular semantics (t pɣa 'land reclamation') as well as of the the two action nominals with irregular phonology. These three examples will be relevant to our hypothesis on the origin of the antipassive in section 4.

Irregular semantics

The transitive pɣa 'to turn around, turn over' has numerous meanings. It can be applied to sheet-like objects, and with clothes it can even mean 'to wear inside out'. It has other specialized meanings like 'to cross a mountain', 'open the cover/lid' or 'to plough a field', with different directional prefixes.

(10) ndʑi-p rt The meaning 'to plough' is always associated with directional prefixes indicating the 'upstream' direction (the same as all verbs meaning 'to dig' in the language):

(12) t ji field la-pɣa pfv:3→3:upstream-turn.over 'He ploughed the field.'

On the other hand, the nominalized form of the verb only has one meaning: the action of reclaiming land by ploughing for the first time (in Chinese 开荒 kaihuang), as illustrated by the following example from the Flood myth:

(13) t -pɣa nmlz:action-turn.over lo-tɕ t-ndʑi evd:upstream-take.out-du 'They du reclaimed land.' (The flood, 85)

Irregular phonology As the argument nominals discussed in 2.2.1, there are also a few action nominals with irregular phonology. First, the transitive verb ntsɣe 'to sell' has an action noun t tsɣe 'commerce' which presents a stem /tsɣe/ distinct from that of the base verb in lacking a n-. An explanation for the additional nin ntsɣe 'to sell' will be proposed in section 4.4.

Second, the possessed noun -n a 'debt' appears to be related to the verb a 'to owe' but it lacks a derivational t -prefix and has a additional nelement. 11 In the following, we will show that this nis a trace of the derivational t -prefix.

We saw in section 2.2.1 (Table 4) that irregular argument nominals were formed by deleting the vowel of the derivational prefix and applying automatic phonological changes to the prefixed stop (k -becomes ɣor xin these nouns). We mentioned that comparative evidence with Situ Rgyalrong indicate that velar and labial stops underwent fricativization in Japhug when occurring as first member of clusters having an obstruent as second member. In the case of coronal stops however, clusters with / t/ or /d/ followed by a consonant other than a non-nasal sonorant exist in Japhug in internal position (though mainly in loanwords from Tibetan across morpheme boundaries).

Let us now observe the synchronic distribution of clusters which have a nasal as second member in Japhug (data from Jacques 2004). We see that there are no clusters with a nasal velar as the first element (* m-, * n-) but that on the other hand there are no clusters with a dental or a labial non-nasal (* n-, *tn-). Moreover, nas the first element of a cluster has a very restricted distribution. It occurs only (i) before a coronal stop or affricate (clusters such as /nt -/, /nts-/ etc, where it is the realization of the homorganic nasal archiphoneme /N/), (ii) before voiced prenasalized stops (/nmb/ and /n g/, transcribed as nband ngin this work) (iii) before nasal consonants (the examples in Table 7). nis conspicuously absent as the first element of a cluster before labial and velar stops (outside of the voiced prenasalized one). Thus, one does not find clusters such as *np-or *nkin Japhug.

If nas first element of a cluster in cases (ii) and (iii) originated from *n-in pre-Japhug, there would be no reason why only nmband nmare possible while *np-and *npare not. A solution to this paradox is to assume that nin cases (ii) and (iii) originate from */t/, which underwent retrograde nasality assimilation, as indicated in table 8. The best evidence for this sound law comes from loanwords from Tibetan, where internal t+nasal clusters automatically undergo these changes (for instance Tibetan mtɕ od.me 'traditional lamp' and rgod.ma 'mare' were borrowed as mtɕ nmi and rgonma). 12 Thus, equipped with this sound law, it is possible to reconstruct -n a 'debt' as *t a in pre-Japhug, a form coming from the expected regular form *t a by loss of the vowel. This is the only known case in Japhug when a action nominal prefix t -undergoes irregular vowel loss.

This particular example will be relevant to our discussion in section 4 on the origin of the antipassive in Japhug.

Bare infinitive and derived inalienably possessed nouns

Besides t -prefixed nominals, we also find another type of action nominal: bare infinitives. These non-finite forms are formed by combining the bare base stem with a possessive prefix coreferent with the patient, as -mto in (14). Only transitive verbs can form bare infinitives (intransitive verbs use k -prefixed forms in the same contexts). ( 14 We also find bare infinitives instead of action nominals with the verb ʑa 'to start' when the patient is an overt noun phrase, as in example 15.

(15) t scoz letter -r t 3sg.poss-bare.inf:write pa-ʑa pfv:3→3-start 'He started writing a letter.' (elicited)

The bare infinitive can also be used as an action nominal in combination with the noun ts ɣa 'form, appearance' as in example ( 16). ( 16) ndʑi-mi 3du.poss-foot -ts o 3sg-bare.inf:attach.to -ts ɣa 3sg.poss-form n ra top:pl wuma very ʑo emph na tɕ ɣ-ndʑi. npst:similar-du 'The way their feet (of fleas and crickets) touch the ground is very similar.' (the cricket 17)

In addition to bare infinitives, there is a rarer formation of bare action nominalizations by prefixation of possessive prefixes to the bare stem of verbs; the indefinite possessor is either t -or t -(Table 9). Given the absence of morphemes other than the possessive prefixes, it is legitimate to wonder whether the direction of derivation in the examples in Table 9 is indeed from verb to noun as posited here. The proof that this is indeed the correct direction of derivation is the fact that the verb fka 'to cover' is borrowed from Tibetan bkab, the past tense form of the verb gebs 'to cover'. The noun -fka 'cover' is clearly secondary and was created within Japhug, as there is no such corresponding noun in Tibetan.

Transitivity in Japhug

Since the focus of this paper is on valency-decreasing derivation, it is necessary to provide some information on transitivity marking in Japhug. Japhug, like all Rgyalrong languages, has a very clear distinction between transitive and intransitive verbs, which is reflected in both case marking and verbal morphology. Morphological transitivity is unambiguous and marked in different but congruent ways, some of which have been mentioned above.

First, Japhug is a strongly head-marking language, with person and number of both arguments marked on the verb (Jacques 2010a). Only transitive verbs can receive the inverse prefix wɣ -, the portmanteau prefixes k -(2→1), ta-(1→2), the perfective direct 3→3' aprefix or the 1/2sg→3 -t suffix (the latter only occurs in open-syllable stem verbs).

Second, Japhug has ergative flagging: S and P are unmarked (examples 17 and 18) , while the A of a transitive verb receives the clitic k (example 18). This clitic is obligatory with nouns and third person pronouns, but optional for first and second person pronouns. The k clitic can also be used to mark instruments. ( 17 Third, some transitive verbs present a special stem in direct 123sg→3 forms. The regular pattern is that verbs whose stem is in -o, -u, -a andchange to -m, -e, -e and -i respectively. This stem alternation does not occur with intransitive verbs.

Fourth, argument nominalisation of transitive and intransitive verbs present tripartite alignment, as the S nominalization is marked by k -, while A nominalization is marked by a possessive prefix followed kand P-nominalization by k -(section 2.2.2). Argument nominalization can therefore always be used to distinguish transitive from intransitive verbs.

There are a few labile verbs is Japhug, and all present agent-preserving ambitransitivity (Jacques 2012b: 217-9). When used intransitively, labile verbs are interpreted as having an undefined patient, as in example ( 19 There are three ways to have an unspecified patient with a non-labile transitive verb. First, the generic human marker k -can be prefixed to the verb. 14 Second, an indefinite pronoun such as t ci 'something' can be used. Third, the verb can be intransitivized by means of an antipassive prefix.

Example 21 illustrates a switch of use between the antipassive s -and the generic k -across two sentences. -u. const-be '(Rabid dogs) bite people without discrimination, and if one is bitten by them, there is poison (in their bites) and one gets infected.' (Rabies, 8) This sentence shows that using the generic form allows anaphoric reference (the P of the verbs a-k -k -mts ɣ 'if one is bitten' and -k -ɕte 'one gets infected' must be the same generic referent), while the antipassive implies that the deleted P is not identifiable (on this topic see Cooreman 1994: 52) and no anaphoric reference is possible.

Antipassive in Japhug

Two productive antipassive prefixes are found in Japhug: r -and s -. 15 The former is used to delete a non-human patient (ɕar 'to search' → r -ɕar 'to search for things') while the second is used to delete a human patient (ɕar 'to search' → s -ɕar 'to search for people'). 16 The patient cannot be reintroduced with oblique case in Japhug antipassive constructions, except for some ditransitive verbs (3.2) . Labile verbs cannot form antipassives.

As illustrated in table 10, the formation of the non-human r -antipassive is perfectly regular (it has an allomorph rabefore a uvular fricative in closed syllables), except for the verbs a 'to owe" and ntsɣe 'to sell', the first of which is discussed in detail in section 4.1.1. The non-human antipassive r -detransitivizes transitive verbs, and the S of the derived verb corresponds to the A of the base verb: this is an agentpreserving derivation, unlike the passive and anticausative. The verb takes an intransitive conjugation and the S appears without ergative marking: The human antipassive s -prefix presents the allomorph sabefore a uvular fricative in closed syllables and the optional variant s zin a few verbs whose stem begins in ɣ -. In the closely related Tshobdun language, ? reports two distinct patientsuppressing s -prefixes, 17 the human antipassive s -(deriving action verbs, as nt e 'to kill' → s -nt e 'to do killing (of people)') and a prefix s -deriving stative verbs meaning 'to have a propensity for V-ing' (t u 'to gore' → s -t u 'to have a propensity for goring (people)').

In Japhug, the situation is very similar to that of Tshobdun, but it is unclear whether two distinct prefixes must be posited. Human antipassive verbs can be either action verbs or propensity stative verbs depending on the context.

For instance, the human antipassive s -sat of the transitive verb sat 'to kill' can be both used as a propensity stative verb s -sat 'have a killing power' (example 23) or as an action verb 'to kill people' (examples 24 and 25). It should be noted that the implied patient of propensity stative verbs is generally human, but in some cases can be applied to animals as well. For instance s -sat 'have a killing power' can designate the killing of both animals or people. In general, human antipassive verbs appear to allow both meanings. For instance, the antipassive s -mts ɣ derived from mts ɣ 'to bite' means both 'to have a propensity for biting people' and 'to bite people' depending on the context. Depending on the meaning of the base verb, some human antipassive verbs will more commonly tend to be action verbs; for instance, s -ɕar, the antipassive of ɕar 'to search', is usually an action verb 'to search for people' and cannot really be interpreted as meaning 'to have a propensity for searching for people' but this is probably more for pragmatic reasons than morphosyntactic ones.

Thus, we will not distinguish in this paper the action human antipassive from the stative antipassive, as this distinction in Japhug reflects specific uses of a single derivation rather than distinct derivations. The tendency of the antipassive construction to express repeated or habitual action rather than a punctual event is well attested cross-linguistically (cf Cooreman 1994: 91-2).

Compatibility with other derivational prefixes

Jacques 2012c describes the Japhug verb in terms of the template in Table 12 (Jacques 2012c). This table represents finite verb forms. In nominalizations, the prefixal slots 1, 5, 6 and all suffixal slots, which mark TAM and person, cannot be filled. Nominalization prefixes described in 2.2 always occur between slots 4 and 5. As indicated in Table 12, antipassive prefixes occur after the causative prefix, but before the tropative and denominal prefixes.

a-m - ɕ - t - t -wɣ- -s -r -n -a- n - - noun Σ -t -a -n m - ɣ -p - s - r - -ndʑi etc.
t - p - l - t - k - n - j -, tu-pj - lu-c - ku- - ju-) permansive n -, ap- prehensive ɕ -
Example 26 illustrates the combination of an antipassive after the zallomorph of the causative prefix.

(26) Daihao p.n. ɣ gen -ɕa pu 3sg.poss-friend n top k erg -wɣ-sqar evd-inv-ask.to.do tɕe coord pj -wɣ-z-r -r t evd-inv-caus-antipass-write -u. ipfv-be 'A friend of Daihao's asked him to draw paintings.' (The painter and the shepherd boy, 10)

The verb z-r -r t 'to cause to make drawings/writings' derives from the antipassive r -r t 'to make drawings/writings' of the transitive verb r t 'to paint, to write'.

The reversed prefix order, namely antipass-caus-, appears to be attested in one example: r -j-ts i 'to give (to) people to drink'.18 However, this example is not a real counterexample to the verbal template in Table 12.

The antipassive r -j-ts i derives from the irregular causative j-ts i 'to give to drink' of the verb ts i 'to drink'. However, this is a lexicalised causative, and there is no compelling evidence for considering the element jas a causative prefix synchronically; the regular causative s -ts i 'to cause to drink' with fully predictable semantics also exists, 19 and there is no other example of the allomorph jof the causative prefix.

The antipassive cannot occur to the left of a regular causative prefix; forms such as *s -s -ts i or *r -s -ts i (intended meaning 'to cause someone to drink' or 'to cause to drink something') are categorically rejected by native speakers.

There are three examples of antipassives combined with the tropative n -, a prefix that derives a transitive verb meaning 'to find ..., to consider ...' from a stative verb. For instance, s -n -mpɕ r 'to consider people beautiful' derives from the tropative n -mpɕ r 'to find beautiful' of the verb mpɕ r 'to be beautiful'.

Finally, the antipassive prefixes commonly appear before denominal prefixes. For instance, the verb s -n -lu 'to trick people' derives from the transitive denominal verb n -lu 'to trick' which itself originates from the inalienably possessed noun -lu 'trick', a loanword from Tibetan blo 'mind, method, trick'.

Combinations of antipassive prefixes with other prefixes are not attested in our present corpus, but this is mainly due to issues of performance (to think of an appropriate context where a word combining for instance antipassive, tropative and de-experiencer could be used) than an effect of grammatical constraints on prefix combination.

Antipassive of secundative ditransitive verbs

Ditransitive verbs in Japhug never mark more than two arguments on the verb, and most present indirective alignment: the theme (the given entity) is coded in the same way as the patient of a monotransitive verb. 20 These verbs are attested with both human and non-human antipassive; for instance t u 'ask' yields both r -t u 'ask something' and s -t u 'ask someone in marriage'. The antipassive cannot be used to delete the recipient for indirective verbs.

However, there are also two verbs with secundative alignment, whose recipient is coded as the patient of a monostransitive verb (mbi 'to give' and jts i 'to give to drink'), as shown in example 27.

( The two verb forms ́-wɣ-mbi-a-ndʑi 'they du gave me' and ́-wɣ-jts i-a-ndʑi 'they du gave me to drink' are 3du→1sg, and the theme is not marked on either verb.

Since recipients are prototypically human, one would expect that the antipassive of these secundative ditransitive verbs would be formed using the s -human antipassive. However, when they undergo antipassivization, these verbs take the prefix r -instead of s -. The theme can be present in the sentence, though the verb is morphologically intransitive, and the agent is not marked in the ergative. Thus, in 28, had the verb been transitive a transitive past suffix -t would have been expected between the verb stem and the personal suffix.21 (28) sto bean n -r -mbi-a pfv-antipass-give-1sg I gave beans (to someone).

In 28, the recipient is unspecified, but unlike antipassive verbs derived from simple transitive verbs, it can be reintroduced with an oblique case (dative marking):

(29) aʑo 1sg t -tɕ indef.poss-boy ra pl n -ɕki 3pl-dat c a alcohol -r -j-ts i-a ipfv-antipass-caus-drink-1sg gr l n.pst:be.usually.the.case I usually give drinks to the guys.

Constructions like 29 with antipassive and an overt recipient are uncommon but can be elicited.

Denominal prefixes

Japhug has a rich array of denominal prefixes, two of which are formally identical to the antipassive r -and s -. This homophony raises the question whether these prefixes are diachronically related, which will be discussed in 4.

In this section, we offer general information on denominal derivations and describe in more detail the r -and s -derivations specifically.

Denominal derivation

There is no evidence of denominal zero derivation in Japhug; derivation from noun to verb requires the addition of one of the seven denominal prefixes (Jacques 2012c: 1217, cf Some of these prefixes present two allomorphs, one with vocalism and the other with vocalism. When the base noun is inalienably possessed, the vocalism of the denominal prefix generally follows that of the indefinite possessor: when the base noun has t -, the derived verb will have a denominal prefix in r -, n -, s -or ɣ -, and when the base noun has an inalienably possessed prefix in t -, the denominal verb will have the series of prefixes r -, n -, s -or ɣ -. This rule however has a few exceptions.

For quantifier nouns and all other nouns, both and denominal prefixes are attested.

Denominal r -prefix

The denominal r -/r -prefix is very productive, and generally used to derive intransitive verbs out of a noun. Verbs derived with this prefix can refer to the production of the entity designated by the base noun either by active building (as in the example 'make a nest' in table 17) or by spontaneous effect ('to have a skin'). In a few cases, r -/ r -can be used to derive a verb meaning 'becoming noun' (as in 'to become a nun'). Finally, it can derive either transitive or intransitive verbs whose meaning is to perform the activity referred to by the base noun ('harvest' → 'to harvest'). The distribution of the allomorphs r -/ r -generally follow the rules presented in the previous section. Inalienably possessed nouns with tindefinite possessor and quantifier nouns always have a denominal verb in r -; inalienably possessed nouns and other nouns can have either r -or r -. Table 18 provides a complete list of types of denominal verbs in r -or r -. From this list, it appears that transitive verbs are less common than intransitive ones (5 out of 25), and among these transitive verbs three are derived specifically from quantifier nouns such as t -spra 'one handful'.

The prefix r -/ r -is extremely productive and can be applied to Chinese loanwords, in which case it always derives an intransitive verb. There are no other derivational prefixes r -or r -in Japhug.

Denominal s -prefixes

The denominal verbs in s -/ s -can be either transitive or intransitive, and belong to four semantic categories: property, position, use of an instrument or body part, and causative, as presented in table 19. The intransitive verb s -mbr 'to become angry' derived from the possessed noun t -mbr 'anger' has an irregular causative form s -z-mbr 'to anger', with the causative prefix -zinserted between the denominal prefix and the root. This causative form is highly regular and isolated, and constitutes an exception to the template presented in Table 12.

Apart from its denominal use, s -can derive transitive verbs out of ideophones. 25 For instance, out of the ideophone lts lts t 'slightly vibrating (as hair, small threads)' (basic root lts t), one can derive the transitive verb s -lts lts t 'to shake slightly'. This derivational process is extremely productive.

Additionally, we find two other homophonous prefixes. One simply results from the fusion of the causative s -with the passive aand will not concern us here ( mbi 'to give', jts i 'to give to drink' → s --mbi 'to ask to be given something', s --jts i 'to ask for something to drink').

The other s -prefix, the de-experiencer, derives a stative verb out of an intransitive or a transitive verb. When applied to an intransitive verb, the S of the base verb is deleted and replaced by the stimulus. For instance, from the intransitive verbs gio 'to slip', scit 'to be happy ' which can have a human S, one derives s -gio 'to be slippery' (of the ground) and s -scit 'to be nice' (of an environment, situation). In the case of transitive verbs, the S of the de-experiencer verb corresponds to the O of the base verb (cf. Jacques 2012b). 26 We will see in section 4.2 how the human antipassive, the denominal s -and the de-experiencer are relatable historically.

Phonotactic constraints on derivational prefixes

In Japhug, derivational prefixes present important phonological constraints, limiting the number of possible forms. These prefixes are either mono-or disyllabic, the possible vowels are , and more rarely a, and out of the 49 consonant phonemes, only nine (m n r s/z ɕ/ʑ j ɣ)27 are found in verbal derivational prefixes.

These strong phonotactic constraints suggest that, whatever the historical origin of these prefixes, they have undergone phonetic attrition and a series of mergers specific to the prefixal position that may have blurred their historical origin.

Thus, the mere fact that two prefixes share a common pronunciation and related semantics is not sufficient to prove that they are historically related, as the probability of chance resemblances is too high. In the following section, we will therefore focus on irregular derivations, as irregularities are the most efficient tool to test historical hypotheses (Schindler 1972).

Evidence for the denominal origin of the antipassive prefixes

As presented in the introduction of this paper, several origins have been documented for antipassive markers cross-linguistically: reflexive, reciprocal, indefinitive person, and light verbs. It appears that none of these can explain the origin of Japhug antipassive markers in a straightforward way. Japhug has specialized and productive reflexive (the ʑɣprefix, see Jacques 2010b) and reciprocal (the aprefix with reduplication of the last syllable of the verb stem) constructions, and none bear any phonetic resemblance to the antipassive prefixes. As for indefinite person, Japhug has a dedicated generic construction (with ergative alignment k -prefix for S/O and wɣfor A, see Jacques 2012b) and an indefinite determiner ci, none of which has any similarity with the antipassive forms. Finally, although examples of verbal prefixes originating from verbs have been documented in Japhug (in particular the associated motion prefixes, see Jacques 2013), of all the light verbs found in the Rgyalrong languages, none bears any similarity to the antipassive markers. 28 On the other hand, we have shown that both antipassive markers are phonetically similar to denominal prefixes. This surface resemblance, though not conclusive by itself, is at least a necessary preliminary condition to investigating whether the two sets of prefixes (antipassive and denominal) can be related.

The following hypothetical derivation path in two stages can be proposed to account for the relationship between these prefixes: 1. A transitive verb is nominalized into an action nominal.

2. The action nominal is turned into a verb by a denominal construction deriving intransitive verbs.

Thus, although in this hypothesis antipassive prefixes do not originate from light verbs, this scenario is in fact very similar to that proposed for West Greenlandic and Mande. An equivalent of stage 1 was present in West Greenlandic, since all three antipassive suffixes originate from the fusion of a nominalization / participial suffix followed by a verb. In Mande, no such stage can be detected, but this is probably due to the fact that these languages allow zero derivation between noun and verbs.

Stage 2 corresponds to the use of a verb meaning 'make' or 'get' in Mande and Eskimo, which are in these cases periphrastic denominal constructions, but can be applied to affixal denominal constructions such as those found in Japhug.

Japhug would thus only differ from the West Greenlandic situation in that the denominal markers cannot be etymologized as coming from verbs.

In the following sections, we evaluate whether this scenario is applicable to the case of Japhug. We first discuss the status of action nominalization in Japhug (the intermediate stage of the hypothesized grammaticalization pathway), and then present several idiosyncrasies which would be unexplainable without the grammaticalization scenario outlined above.

Non-human antipassive

In Japhug, as seen in section 2.2, almost all deverbal nouns are marked with a specific derivational prefix, and thus any denominal derivation should preserve the nominalization prefix. This is indeed verified for cases such as n k ma 'to be wrong (vi)', a denominal verb derived from k -ma 'which is not', the S-nominal of ma 'not to be' as well as the verbs in Table 16. It is clear that the antipassive prefixes r -and s -cannot have originated from such nominalized forms.

Nevertheless, in section 2.2.3, we saw that a few nominalized forms are simply formed by converting the bare verbal stem to inalienably possessed nouns, always taking possessive prefixes (bare infinitives and bare action nominals).

Thus, the antipassive r -ɕp t 'to patch clothes' of the transitive verb ɕp t is actually synchronically ambiguous. It could be perfectly well analysed as the denominal derivation in r -from the inalienably possessed -ɕp t 'patch', the bare action nominal derived from ɕp t.

That this analysis is indeed possible is confirmed by the fact that the only bare action nominal whose indefinite possessive prefix is t -(not t -), -s so 'thought', has a derived denominal verb r s so 'to think (vi)' in r -. 29 From both the point of view of phonology and semantics, it is possible to assume that the denominal prefix r -arose from a development in two stages:

1. Transitive verb → bare action nominal (ɕp t 'to patch (vt)' → -ɕp t 'patch (n)')

2. bare action nominal → intransitive denominal verb r -ɕp t 'to patch clothes'

It is not necessary to assume that a derivation in several stages occurred for all antipassive verbs. It suffices to have a critical mass of ambiguous pivot forms such as r -ɕp t for the prefix r -to undergo reanalysis from denominal to antipassive. After reanalysis took place, the two prefixes became entirely distinct, and they do not even belong to the same slot in the verbal template in Japhug as spoken today, as we saw in section 3.1.

Any historical hypothesis must not only account for regular development, but should also provide an account for irregularities. In the following, we show that some common irregularities between action nominals and antipassive verbs can be explained by a series of stages involving nominalization followed by denominal derivation.

Irregular phonology

As seen in section 3.3.2, only two antipassive verbs have a phonologically irregular form, one for which is r -n a 'to owe money" from the verb a 'to buy on credit, to owe'.

The transitive verb a takes as its object the amount of money owed (not the person to whom the money is owed):

(30) sq -mpɕar ten-leaf k -a-t-a pfv-owe-pst:tr-1sg 'I (bought it on tick and) owe ten yuan.'

With the antipassive r -n a, the amount owed cannot be specified. The antipassive form is irregular in that an extra element nappears between the antipassive prefix and the verb root. It is noteworthy that the inalienably possessed noun -n a 'debt' has the same irregularity as the antipassive form. In section 2.2.2, we saw that this nis an irregular allomorph of the action nominalization prefix t -with irregular syncope (-n a < *t a).

The indefinite possessive prefix associated with -n a is t -(thus t -n a 'someone's debt'), but we saw in section 3.3.1 that inalienably possessed nouns form their denominal verbs with either the or the allomorph of the denominal prefixes. Thus, r -n a 'owe a debt' is a possible outcome for the denominal derivation of -n a 'debt'. Just like r -ɕp t 'to patch clothes' above, it is a synchronically ambiguous form.

While in the case of r -ɕp t 'patch clothes' one could argue that the resemblance between the antipassive marker r -and the intransitive denominal prefix is fortuitous, this option is not available in the case of r -n a 'to owe a debt'. The common irregularity between the nominal form -n a 'debt' and the verb r -n a 'to owe a debt' shows that r -n a cannot have been directly derived from the base verb a 'to owe', and that the inalienably possessed noun -n a 'debt' was the intermediate stage of derivation.

Unlike r -ɕp t 'to patch clothes' above, the pathway of derivation occurred in three stages:

1. a 'to owe' → action nominal *t -a 'debt' 2. conversion into an inalienably possessed noun with syncope of the prefix vowel *t -a → *-t-a → -n a '(someone's) debt'

3. denominal derivation from the inalienably possessed nominal into an intransitive verb -n a → r -n a 'to owe a debt'

This example shows that while the basic scenario action nominalization + intransitive denominal derivation for the origin of the Japhug antipassive accounts for the observed data, the bare action nominals in t -are not necessarily the only intermediate nominalized stage of this grammaticalization pathway.

Irregular semantics

The transitive verb pɣa 'to turn around' has an antipassive r -pɣa 'to reclaim land' which is not irregular phonologically like the previous example, but has semantics which are much more restricted than that of the base verb.

The irregular semantics, here again, is not specific to the antipassive form: it is shared with the action nominal t -pɣa which means 'land reclamation' and not 'turning over' as would be expected (cf section 2.2.2). This commonality shows that the action nominal and the antipassive form are related. Two hypotheses could be put forth to explain this common innovative meaning: either the antipassive is a denominal verb derived from the action nominal in t -, or both the action nominal and the antipassive are linked to one another by a third form which was lost in the modern language. 30 The first hypothesis, derivation from an action nominal in t -, is problematic: as we saw in section 3.3.1, there are two examples of denominal verbs from action nominal, and they preserve the t -derivational prefix (t -sqa 'wheat porridge' → r -t -sqa 'to have wheat porridge', cf table 16). The expected denominal verb from t -pɣa 'land reclamation' would thus be unattested †r -t -pɣa instead of r -pɣa 'to reclaim land'.

The second hypothesis would imply the existence of a possessed noun *-pɣa 'reclamation of' (a particular place), from which r -pɣa would be directly derived. This noun could simply be the bare infinitive derived from pɣa : we saw that a synchronic alternation between action nominals and bare infinitives is still productive in complements of the verb ʑa 'to start' (see example 15, section 2.2.3).

We have shown that the r -non-human antipassive in Japhug can be explained as originating from the reanalysis of the denominal prefix rapplied to inalienably possessed action nominals deriving from transitive verbs. Reanalysis occurred either from a bare action nominal, the bare infinitive or from an inalienably possessed nominal derived from the taction nominals which underwent vowel loss and cluster coalescence.

The fact that this hypothesis explains common phonological and semantic irregularities between action nominals and antipassive verbs is a confirmation that the formal resemblance between the antipassive and the denominal prefixes is not a coincidence, but that the two constructions are historically related.

Human antipassive

In the previous section, we showed that the non-human antipassive rprefix was historically derived from the denominal r -/ r -prefix. It is thus legitimate to attempt to apply the same explanatory model to the human s -antipassive.

In section 3.3.1, we saw that a denominal prefix derives intransitive stative verbs designating an intrinsic property or mental state in examples such as -nd ɣ 'poison' → s nd ɣ 'to be poisonous'.

This derivation is semantically very close to the stative propensity antipassive described in 3. Using the same chain of derivation as for the rantipassive, we propose the following scenario to explain the origin of the human antipassive in Japhug:

1. As in the case of the r -antipassive, a transitive verb is turned into a inalienably possessed bare action nominal or a bare infinitive. (sat 'to kill' → -sat 'killing')

2. The action nominal undergoes denominal derivation with the prefix s -into a property stative verb. (*-sat 'killing' → s -sat 'to have a propensity to kill, to have killing power').

3. This stative verb is reanalyzed as an action verb due to some ambiguous contexts (s -sat 'to have a propensity to kill' → s -sat 'to kill people').

The de-experiencer s -described in 3.3.3 can be explained as having undergone the same steps of reanalysis, except that the re-alignment of syntactic primitives occurred in a different way (S=A of base verb in the case of antipassive, S=stimulus in the case of de-experiencer).

Unlike the case of the r -antipassive, for the human antipassive we do not have any irregular verb showing shared idiosyncrasy between action nominal and human antipassive or de-experiencer as the examples discussed in sections 4.1.1 and 4.1.2. Thus, this hypothesis, while plausible, cannot be considered to be fully demonstrated until such an example is discovered.

A chain shift?

The presence of two antipassives in Japhug raises the question of how systems with human vs. non-human antipassive come into being. To our knowledge, only one case has been discussed in the literature, that of Nahuatl te-'human antipassive' (generally called 'indefinite human object') vs. tla-'non-human antipassive' ('indefinite non-human object'). 31 We will describe the Nahuatl data and then compare them with Japhug to evaluate whether the two languages attest the same type of evolution.

A detailed study on the etymology of the Nahuatl antipassive tlaand teprefixes is still lacking, but these prefixes have clear cognates in other languages and can be reconstructed to proto-Uto-Aztecan. Langacker (1977: 46) argues that the prefixes *ta-'unspecified subject' and *t -'unspecified object' can be reconstructed in proto-Uto-Aztecan. The *ta-'unspecified subject' prefix itself is probably related to the indefinite pronoun *hita 'something' (Langacker 1977: 120).

In Nahuatl these prefixes yield *ta-→ tla-'non-human antipassive'32 and te-'human antipassive', with a chain (push) shift:

• generic agent → non-human antipassive • antipassive → human antipassive By contrast, there is no evidence in Japhug that such a chain shift took place. The difference of meaning observed in the two antipassives r -and s -directly reflects that of their corresponding original denominal prefixes r -/ r -(production / action) and s -(property of the base noun to which humans can be susceptible).

The fact that secundative ditransitive verbs have an antipassive in rinstead of expected s -(see section 3.2) does not imply that antipassive in r -used to be the general antipassive, later superseded by s -for monotransitive verbs. Rather, it is likely that it is due to homophony avoidance with the combination of the causative with the passive s -+ a-→ swhich is found with this type of verbs (as in mbi 'to give' → s --mbi 'to ask to be given'). Since this combination of derivational prefixes is not attested with monotransitive verbs, this homophony avoidance was limited to ditransitive verbs.

Thus, the model of evolution presented in Japhug enriches our knowledge of the possible origins of human vs. non-human antipassive systems, as the development attested in Japhug seems without clear parallel elsewhere.

Other derivations

The pathway of grammaticalization proposed in the previous sections to explain the origin of the antipassive prefixes can also potentially be applied to other voice markers, in particular the applicative n -and causative sprefixes. In this paper, only the case of the applicative will be discussed in detail.

The applicative n -can be illustrated by the examples in Table 21. We also find a denominal prefix n -in Japhug, which mainly derives transitive verbs, as illustrated in table 22. Although a few intransitives derived by the prefix n -are attested, when a pair of transitive and intransitive verbs are derived from a single noun, the productive pattern is to have an intransitive verb in r -/ r -and a transitive one in n -, as illustrated in table 23 with Tibetan loanwords.33 It is therefore possible to propose that the applicative resulted from the reanalysis of a denominal derivation of an action nominal as in the case of the antipassive prefixes.

Indeed, the mechanism of reanalysis illustrated in this paper concerning the antipassive derivation appears to be a common, but poorly recog-nized, grammaticalization path leading to various voice markers, including antipassive and applicative, but not restricted to these two. Languages with rich denominal derivation systems have the possibility of creating new voice markers by combining the appropriate nominalized form with a denominal marker.

Conclusion

The present paper contributes to the general theory of grammaticalization in documenting a previously unreported origin for voice markers. It shows that voice markers, in particular the antipassive but also potentially the applicative and other ones, can be formed historically out of a double derivation:

(31) nominalization + denominal derivation ⇒ voice derivation More specifically:

(32) action nominalization of transitive verb + intransitive denominal derivation ⇒ antipassive (33) action nominalization of intransitive verb + transitive denominal derivation ⇒ applicative / causative

The reason for this derivation in two steps is that action nominalization first neutralizes the original transitivity of the verb root, and a new transitivity value is allocated by a specific denominal derivation.

Figure 1 :

 1 Figure 1: Rgyalrong languages

(

(

  22) t -rʑa indef.poss-wife n top pj -r -ɕp t evd-antipass:non.human-mend 'The wife mended (clothes).' (The raven 19)

  (23) n n this wuma very ʑo emph -s -sat const-antipass:human-kill 'Its killing power is considerable (of a gun).' (Guns, 117) (24) k -s -sat inf-antipass:human-kill pj -r o evd-experience 'He has killed [a man] before.' (In Chinese: 他杀过人) (25) k -s -sat nmlz:S/A-antipass:human-kill jo-ɕe evd-go 'He went to kill [people].'

  1sg/2sg transitive -t (past tenses) 17. 1sg -a 18. Personal agreement suffixes (-tɕi, -ji, -n , -ndʑi)

Table 1 :

 1 Attested sources of antipassive markers

	origin	example	reference
	reflexive benefactive / malefactive reciprocal / coparticipation Tswana Slavic, Romance, West Mande, Pama-Nyungan Eskaleut indefinite, generic argument Nahuatl TAM non-telic Godoberi verb make West Mande, Eskaleut Creissels (2012) Nedjalkov (2007), Say (2008: 378-517) Creissels (2012) Terrill (1997) Jacobson (1984: 453), Mithun (2000: 97-8) Creissels and Nouguier-Voisin (2008) Langacker (1977: 46) Tatevosov (2004) get

Table 2 :

 2 Pronouns and possessive prefixes

	Free pronoun	Prefix	Person
	aʑo, j n ʑo, n j ʑo tɕiʑo ndʑiʑo ʑ ni iʑo, iʑora, iʑ ra n ʑo, n ʑora, n ʑ ra n -a-n --tɕi-ndʑi-ndʑi-i-ʑara n -t ʑo t -	1sg 2sg 3sg 1du 2du 3du 1pl 2pl 3pl

or t -/taindefinite / generic

Table 4 :

 4 Irregular nominalizations in ɣand x-

	noun	meaning	base verb meaning
	ndʑ -a --xso	disastrous fire ndʑ disaster a orifice empty thing so	burn be black be opened be empty

Table 5 : Sporadic vowel attrition in the animal class prefixes in Japhug

 5

	Japhug	meaning	Situ
	k -rts ɣ leopard k -ɕpaz marmot ɣ-z monkey -ni flying squirrel ka-i k -ɕtɕ k k -p s k -tsuɣ The
	examples in Table 5 suggest that vowel attrition only takes place in words whose second syllable has a simple onset (does not begin in an

Table 6

 6

	illustrates the most representative examples of such irregular nouns. Apart from numerous examples with irregular semantics, we also find two examples with irregular phonology.
	Table 6: Examples of irregular action nominals and their base verbs noun meaning base verb meaning irregularity
	t sqa t pu t pɣa t tsɣe commerce wheat porridge moxibustion land reclamation pɣa sqa pu ntsɣe -n a debt a	cook cook in ashes id. semantics turn over id. sell phonology owe id.

Table 7 :

 7 Clusters with a nasal as a second member in Japhug

	labial dental velar
	labial dental nm-velar ɣm-	mn-ɣn-	m -n -

Table 8 :

 8 Retrograde nasality assimilation in Japhug clusters

	pre-Japhug Japhug
	*tm-*t -*tmb-*t g-	nm-n -nb-ng-

Table 9 :

 9 Bare nominalizations (inalienably possessed nouns)

	base verb meaning noun stem indefinite meaning possessor
	fka ɕp t s so	cover patch think	-fka -ɕp t -s so	t -fka t -ɕp t t -s so	lid patch (n.) thought

  ).

	(19) tɕ eme girl 'A girl was weaving.' (The demon, 28) ci indef p -ta pst.ipf-weave -u const-be
	Non-overt patients of non-labile transitive verbs on the other are al-ways interpreted as a referent previously mentioned in the text. Thus, in a sentence such as 20, the verb tu-ndze (ipf-eat[III]) can only mean 'eat it', never 'eat something'. 13
	(20) t ji field gr l 3sg.poss-inside -ng npst:be.usually.the.case tɕe, lnk tɕe, qapri snake lnk kha k erg house tɕe tu-ndze ipf-eat[III] lnk l lu cat k erg u npst:be 'In the field, snakes eat them (mice) and in the house, cats eat them.' tu-ndze ipf-eat[III] (Mice, 163-4)

Table 10 :

 10 Examples of the antipassive prefix r -

	basic transitive verb	derived intransitive verb
	ro tɕ ɕp t to patch to carve to burn pɣa to turn over t to sew ɕar to search a to owe (a specific quantity) r -n a r -ro r -tɕ r -ɕp t to patch things to carve things to burn land r -pɣa to reclaim land r -t to sew things r -ɕar to search for things to owe money ntsɣe to sell r -tsɣe to sell things t to buy ra-t to buy things

Table 11 :

 11 Examples of the antipassive prefix s -

	basic transitive verb	derived intransitive verb
	ɣ m ɕar tɕ mts ɣ n mtsio nd	to praise s -ɣ m , s z-ɣ m to search s -ɕar to gore s -tɕ to bite s -mts ɣ to peck s -n mtsio to hit sa-nd	to praise people to search for people to gore people to bite people to peck at people to hit people

Table 12 :

 12 The Japhug verbal template (shaded areas indicate derivational prefixes)

Table 13 )

 13 .

Table 13 :

 13 List of denominal prefixes in JaphugWhen inalienably possessed nouns and quantifier nouns undergo denominal derivation into verbs, the possessive prefixes and the numeral prefixes are invariably suppressed, as shown by the examples in Table14.

	Form	Property
	n -, n -r -, r -ɣ -, ɣ -s -, s -, s ɣ-transitive verb with instrument, intransitive verb of position intransitive and transitive intransitive and transitive intransitive and transitive m -transitive verb with body part, intransitive verb of position s -intransitive verb (property) aɣ -intransitive verb (property)

Table 14 :

 14 Examples of denominal verbs from inalienably possessed and quantifier nouns

	Category	Transitivity Derived verb Meaning	Base noun Meaning
	inalienable intr. intr. tr. tr. tr. quantifier tr.	r -g m r -ɕmi n -ɣmaz n -jro s -rmi r -tɣa	to lay an egg to speak to wound to follow a trail to give a name to mesure by span -tɣa -g m -ɕmi -ɣmaz -jro -rmi	egg word wound footprints name handspan

Table 15 :

 15 Vocalism of the denominal prefixesExceptions to the vowel copying principle between indefinite possessor and denominal verb can be found: there are examples of inalienably possessed nouns with t -indefinite possessor whose denominal verbs have vocalism 22 , but the reverse is not true: there are no nouns in t -with denominal verbs in .Action nominal prefixes can be preserved after denominal derivation, as shown in table16.23

	Indefinite noun stem meaning possessor	denominal derived prefix verb	meaning
	t -t -t -t -t -t -t -	-lo -rʑa -p ri -p ri -rmi ɕom -n -ɕt i ftɕ ka t a	nest woman dinner dinner name skin of the milk r -r -n -n -n -s -breast n -sweat s -method r -tea n -	r lo n rʑa n p ri n p ri s rmi r -ɕom n n s ɕt i r ftɕ ka to prepare (vi) to build a nest (vi) to marry (vt) to have dinner (vi) to have dinner (vi) to give a name (vt) to have a skin (of milk) (vi) to suck (vt) to cause to sweat (vt) n t a to have breakfast (vi)

Table 16 :

 16 Action nominal t -prefix preserved after denominal derivation

	Base verb Meaning	Action nominal Meaning	Denominal verb Meaning
	fɕ l sqa	have diarrhoea (vi) t -fɕ l to cook (vt) t -sqa	diarrhoea wheat porridge r -t -sqa n -t -fɕ l	have diarrhoea (vi) have wheat porridge

Table 17 :

 17 Examples of denominal verbs in r -and r -in Japhug (inalienably possessed nouns are indicated with their indefinite possessive prefix t -/t -and the quantifier nouns with the numeral one t -between brackets)

	Category	Transitivity Derived verb Meaning	Base noun Meaning
	inalienable intr. intr. intr. intr. inalienable intr. intr. inalienable tr. quantifier tr.	r -r it r -tɕ m r -qarts r -zga r -s so r -pɕa r -pj z r -spra	to have a child to become a nun to harvest to make honey to think to prostrate oneself pɕa (t )-r it tɕ m qarts zga (t )-s so thought, desire child nun harvest sauce (cf ɣʑ -zga 'honey' ) prostration to plait (t )-pj z plait to take a handful of (t )-spra one handful

Table 18 :

 18 Types of denominal verbs in r -and r -in Japhug

	Form Category	Transitivity Number of examples
	r -r -r -r -r -r -r -r -	production production becoming becoming perform activity intr. intr. intr. intr. intr. perform activity intr. perform activity tr. perform activity tr.	2 9 1 1 9 3 2 4

Table 19 :

 19 Examples of denominal verbs in s -and s -in JaphugThe total count of examples in each category of the s -/ s -denominal derivation in our forthcoming dictionary is listed in table 20.24

	Category	Transitivity Derived verb Meaning	Base noun Meaning
	property position instrument intr. intr. intr. intr. instrument tr. instrument tr. instrument tr. causative tr. causative tr.	s -nd ɣ s -mbr s -ndz pe s -ejlu s -k s -fsa s ɣ-ts a s -ɕt i s -rmi	to be poisonous to be angry to sit (in a special way) ndz pe (t )-nd ɣ poison (t )-mbr anger way of sitting be left-handed ejlu left hand to smoke (t )-k smoke to perform fsa fumigation ritual fumigation to sieve ts a sieve to cause to sweat (t )-ɕt i sweat to give a name (t )-rmi name

Table 20 :

 20 Types of denominal verbs in s -and s -in Japhug

	Form	Category	Transitivity Number of examples
	s -s -s -s -s -s ɣ-s -/ sa-use of an instrument / body part tr. property / mental state intr. position intr. use of an instrument / body part intr. use of an instrument / body part labile use of an instrument / body part tr. use of an instrument / body part tr. s -causative tr. s -causative tr.	4 2 1 2 6 3 3 2 1

Table 21 :

 21 Examples of the n -applicative prefix

	base verb	derived verb
	mbɣom ke rga	be hurried n -mbɣom go on foot n -ke like (vi) n -rga	look forward to, miss s.o. look for like (vt)

Table 22 :

 22 Examples of the denominal prefix n -Base noun Meaning Derived verb Meaning

	sɣa qa y -gra mt k j u mb rl n plane rust fish salary spell oath sm n medicine n -sm n n -sɣa n -qa y n -gra n -mt n -k j u n -mb rl n to plane to be rusty to fish to receive a salary to cast a spell to swear to treat mk ɣ r necklace n -mk ɣ r to wear as a necklace vt vi vi vi vt vt vt vt gra enemy n -gra to treat as an enemy vt sk r body n -sk r to be pregnant with vt

Table 23 :

 23 Examples of pairs of denominal verbs

	Base noun Meaning Intransitive	Transitive
	ftɕ ka k ramba	method lie	r -ftɕ ka 'to prepare (vi)' r -k ramba 'to tell lies (vi)' n -k ramba 'to cheat (vt)' n -ftɕ ka 'to prepare (vt)'

See Janic (2013) for a review of the terminology used to refer to antipassive constructions in accusative languages. Some authors restrict the definition of antipassive constructions to ergative languages (for instance[START_REF] Dixon | Ergativity[END_REF][START_REF] Cooreman | A functional typology of antipassives[END_REF]

).3 A detailed account of the Nahuatl antipassive is provided in

section 4.3.4 Mithun (2000: 97-8) mentions antipassives deriving from benefactive markers in Yup'ik, but these are not related to the Greenlandic suffixes.

This issue will be discussed in more detail in 4.

This terminology follows works such as[START_REF] Thompson | On the grammar of body parts in Koyukon Athabaskan[END_REF] on Athabaskan languages; see also[START_REF] Sun | Nominal Morphology in Caodeng rGyalrong[END_REF] on the related Tshobdun language.

For instance in Navajo we find a similar opposition between si-ts ' 1sg.poss-flesh 'my

A few minor exceptions are discussed inJacques (2004: 45, 261), but are of no incidence to the present discussion.

In any case, even if counterexamples to this generalization are found, this would not be surprising, as vowel attrition in presyllables and monosyllabicization tend to be a sporadic process in its first stages (see[START_REF] Michaud | Monosyllabicization: patterns of evolution in Asian languages[END_REF].

There are two distinct scholarly traditions on this particular topic,[START_REF] Comrie | The syntax of action nominalizations: a crosslanguage study[END_REF] andKoptjevskaja-Tamm (1993: 5) on the one hand who use the terms 'action nominal' and 'action nominal constructions', and Grimshaw 1990 on the other hand, whose work focusses on the distinction between process and result nominals which is not taken into account in[START_REF] Koptjevskaja-Tamm | Nominalizations[END_REF]. We retain here the term 'action nominal'; this construction would be labelled as 'result nominal' in Grimshaw's framework.

Since -n a is a inalienably possessed noun, its form without definite possessive prefix is t -n a, but the there is the indefinite possessor prefix, and alternates with the series of possessive prefix in Table2.

The Tibetan translitteration used here follows Jacques (2012a).

In this particular example, the non-overt patient is mice as a species, which were referred to previously in the text; in Japhug generic referents can be either singular or plural.

The generic marker for S and P in Japhug is k -, a prefix unrelated at least synchronically to the homophonous nominalization prefix k -(Jacques 2012b: 204-89). Generic marking in Japhug will not be discussed in this paper. Unlike human antipassive, generic patients in k -can be topical, and this form is typically used in gnomic statements and procedural texts.

 15 There is a third antipassive prefix ɕ monly attested with the verb t u 'to ask' → ɕ mt u 'to ask a lot of

questions'.16 A similar situation is found in the closely related language Tshobdun,(Sun 2006: 8), and a typological parallel is observed in Nahuatl which also has a human antipassive teand a non-human antipassive tla-(Creissels 2006: 91).

s -in Tshobdun is the form regularly corresponding to Japhug s -.

See section 3.2 for the reason why r -is present here instead of s -.

The semantic difference between the irregular causative jts i and the regular one s -ts i is very clear. The former specifically means 'to give something to drink to ease thirst', while the second has the full range of meanings of causatives, including 'to force to drink', 'to cause to drink inadvertently' and 'to drink with (an instrument)'.

We follow here[START_REF] Malchukov | Ditransitive constructions: a typological overview[END_REF]'s terminology.

Its transitive equivalent is n -mbi-t-a pfv-give-pst:tr-1sg 'I gave it to him', a form where the recipient is always definite.

For instance ɣm r 'mouth' has the indefinite possessor prefix t -but its denominal verb is n -ɣm r 'to hold in the mouth')

Although both n t fɕ l and fɕ l are translated by the same English gloss, their meanings are different. The first one has human S, while the second must have the body part inalienably possessed noun -xtu 'belly' as its only possible argument.

These figures slightly differ from those presented in Jacques (2012c), as more examples have been found during recent fieldwork.

This phenomenon has been first described in the related Tshobdun languages by[START_REF] Sun | 草登嘉戎語的狀貌詞 Caǒdeng Jiarońgyǔde zhuaǹgmaòci ́(The ideophones in Tshobdun Rgyalrong)[END_REF].

Two Japhug incorporating verbs (s -mbr -g 'to be detestable' and s -ʑ -lo 'to be disgusting') also include the de-experiencer prefix s -. The exact pathway of derivation of these two verbs is described in detail in Jacques (2012c: §4.1).

We could reduce this figure to seven, since the voiced fricatives /ʑ/ and /z/ and their voiceless counterparts /ɕ/ and /s/ are never contrastive in prefixes, and their distribution is always predictable. Two more consonants (/t/ and /k/) appear in non-finite verbal prefixes.

In Japhug the common light verbs are the following: l t 'to throw', zu 'to do', pa 'to do' and ti 'to say'.

We saw in section 3.3.1 that inalienably possessed nouns whose indefinite possessive prefix is t -generally make their denominal verbs in r -while those in t -always have denominal verbs in r -.

The third possibility, namely a derivation from the antipassive to the action nominal, is impossible, as the derivational prefix r -would not disappear.

The analysis of these prefixes as antipassive markers has been proposed byCreissels (2006: 91).

By the application of Whorf's law *ta → tla.

Respectively from Tibetan btɕa.ka 'method' and k ram.ba 'lie'.

funded by the Hi-malCo project (ANR-12-CORP-0006) and is related to the research strand LR-4.of the Labex EFL (funded by the ANR/CGI). Glosses follow the Leipzig glossing rules, except for assert assertive, const constative, lnk linker and inv inverse.


Nesrine Ben Hassine
email: nesrine.ben-hassine@inria.fr

Dana Marinca
email: dana.marinca@prism.uvsq.fr

Pascale Minet
email: pascale.minet@inria.fr

Dominique Barth
email: dominique.barth@prism.uvsq.fr

Popularity Prediction in Content Delivery Networks

Content delivery networks (CDNs) face a large and continuously increasing number of users solicitations for video contents. In this paper, we focus on the prediction of popularity evolution of video contents. Based on the observation of past solicitations of individual video contents, individual future solicitations are predicted. We compare different prediction strategies: SES, DES and Basic. The best tuning of each strategy is determined, depending on the considered phase of the solicitation curve. Since DES and Basic experts outperform the SES expert, our method combines DES and Basic experts to predict the number of solicitations within a phase and automatically detect the phase changes, respectively. This self-learning and prediction method can be applied to optimize resources allocation in service oriented architectures and self-adaptive networks, more precisely for the CDN cache nodes management.

I. INTRODUCTION

With the emergence of media platforms (e.g. YouTube, Daily Motion), multimedia contents have experienced a significant growth of users solicitations. Consequently, the nature of most of the traffic circulating on internet nowadays is a User-Generated Content (UGC) traffic and Video-on-Demand (VoD) content. YouTube is known to be the most popular UGC. YouTube claims to serve 460 million visits per day, whereas Netflix, a VoD system, serves 22 million visits per day. Content Delivery Networks (CDNs) cope with such enormous and growing number of content solicitations by means of caching and duplicating contents near the end users. Indeed, popularity is defined as the relationship between a content and the users who visualize it. The dynamics of content solicitation can be better understood by studying content popularity. To transform observed information in valuable knowledge, one needs to make a step forward and go beyond observing and explaining the past to build models that will predict future behavior.

When a content becomes popular, it will generate an increase in traffic, which in turn can lead to an important delay, or even a saturation of the network. An accurate prediction of a content popularity can help to manage the content storage in a CDN in order to maximize the number of hits and minimize the number of unsatisfied users because of large delays. An inaccurate prediction, on the other hand, can lead to misallocated resources [START_REF] Abrahamsson | Program popularity and viewer behaviour in a large tv-on-demand system[END_REF]. The collective user behavior in terms of content can also be used to build dynamic data replication strategies in order to lighten the traffic directed to the same cache and/or to be closer to different groups of users who request the same content but are geographically distant from each other [START_REF] Applegate | Optimal content placement for a large-scale vod system[END_REF]. Popularity is used to decide on the one hand which content should be cached and if the cache size does not allow storing the new content, which content should be ejected [START_REF] Famaey | Towards a predictive cache replacement strategy for multimedia content[END_REF]. Moreover, studying content popularity can be useful for transport optimization in some applications thanks to hybrid multicast-unicast transport using multicast for the most popular contents and unicast for the less popular programs [START_REF] Meddour | A cross layer architecture for multicast and unicast video transmission in mobile broadband networks[END_REF].

Furthermore, popularity can be used to support enhanced applications that are a source of revenues for the CDN providers. Indeed, popularity is an important measure for online marketing. If the popularity can be predicted accurately, better marketing strategies can be adopted or different advertising rates can be charged. Since popularity indicator is tied directly to ad revenue, revenue might be accurately estimated over time if all parties know how many views a content is likely to attract [START_REF] Kupavskii | {Predicting the Audience Size of a Tweet}[END_REF], [START_REF] Szabo | Predicting the popularity of online content[END_REF]. Thus, predicting content popularity of various contents is of great importance to manage various services and more particularly new services with added values.

In this paper, we present a self-learning and prediction method able to accurately predict the future number of solicitations of individual video contents. For the simulations, we have used real traces on video contents stored on the YouTube website, concerning the daily number of sollicitations since content creation untill now. The method is based on the definition of several experts, each one predicting the future solicitation according to its own strategy. Different prediction strategies are compared: Single Exponential Smoothing (SES) [START_REF] Cesa-Bianchi | Prediction, learning, and games[END_REF], Double Exponential Smoothing (DES) [START_REF] Cesa-Bianchi | Prediction, learning, and games[END_REF] and a basic one (Basic) [START_REF] Ang | Pid control system analysis, design, and technology[END_REF] issued from control theory. For each prediction strategy, the best tuning of parameters is determined. We show the interest of distinguishing phases in the popularity evolution of a video content to improve the accuracy of expert prediction. Our method combines the best DES expert per phase and the Basic expert.

II. RELATED WORK

There have been several research regarding the study of the popularity of multimedia contents. Popularity can be measured in different ways. It is mostly expressed by the number of views over a period of time [START_REF] Szabo | Predicting the popularity of online content[END_REF], [START_REF] Pinto | Using early view patterns to predict the popularity of youtube videos[END_REF], [START_REF] Ahmed | A peek into the future: Predicting the evolution of popularity in user generated content[END_REF], [START_REF] Gursun | Describing and forecasting video access patterns[END_REF] and this is the definition adopted in this paper. Yet, in [START_REF] Schultes | Leave a comment! an in-depth analysis of user comments on youtube[END_REF] feedbacks were the metric used to quantitatively evaluate web content popularity. For instance, comments outline the opinion of users with respect to the content, sharing proves its fame. However, comment analysis requires a semantic study whereas sharing evaluation must be done considering all social networks. Another evaluation of popularity is based on ratings that describe the quality of the content and can provide an estimation of the popularity thanks to an observed correlation between user rankings and content views [START_REF] Gill | Youtube traffic characterization: a view from the edge[END_REF].

Understanding the popularity of contents and the relationship between requests and contents age is fundamental in the design of efficient communication systems. Indeed, a content cannot be requested before it is uploaded and it is expected that even popular contents will not be requested forever. Once published at a given time, a content popularity vanishes over time. Besides, contents exhibit different profiles of popularity [START_REF] Carlinet | Four months in daily motion: Dissecting user video requests[END_REF]: some contents are able to accumulate hundreds of millions of views, whereas the vast majority can only attract a few. Some contents have the same order of popularity magnitude where the average number of solicitations per day is low but covers a lot of days. Some can be highly but shortly popular; others may have been uploaded and/or removed during the same day.

Since the number of views over a period of time is the simplest way to evaluate popularity, we adopt this definition. The popularity prediction is to estimate the number of views associated with a given content at some time in the future, based on its past evolution [START_REF] Ahmed | A peek into the future: Predicting the evolution of popularity in user generated content[END_REF].

Since the understanding of user intents and preferences is key to personalized services, predicting content popularity based on users behavior has been the subject of several researches. Popularity was proved to follow Zipf distribution when analyzing the viewing rate of contents [START_REF] Carlinet | Four months in daily motion: Dissecting user video requests[END_REF], [START_REF] Mitra | Characterizing web-based video sharing workloads[END_REF], [START_REF] Breslau | Web caching and zipf-like distributions: Evidence and implications[END_REF]. In [START_REF] Yu | Understanding user behavior in large-scale video-on-demand systems[END_REF], Yu et al enumerate previous works investigating the application of Zipf's law to web access and prove that the distribution of users request is indeed described by Zipf's law [START_REF] Breslau | Web caching and zipf-like distributions: Evidence and implications[END_REF]. However, Cha et al had found that the number of views is better described by power-law with exponential cut-off. In fact, several studies use real traces to determine the law of the distribution of content popularity. All agree on distribution following a Zipf law for the most popular contents. For less popular contents, popularity is remarkably lower than the predicted popularity using the Zipf distribution [START_REF] Cha | Analyzing the video popularity characteristics of large-scale user generated content systems[END_REF]. To have more accurate results, we use real traces for this study.

This process of prediction encompasses two approaches: the first is to predict the exact value of the popularity. The second approach assumes that we have an idea on the popularity bounds and predicts a class membership where a class includes all contents whose popularity belongs to a given interval.

Analyzing the popularity characteristics of UGC system proves that a strong correlation exists between the popularity of each content at early and later stages during its lifetime. Hence linear regression [START_REF] Cha | Analyzing the video popularity characteristics of large-scale user generated content systems[END_REF] is used as a prediction method. Szabo and Huberman [START_REF] Szabo | Predicting the popularity of online content[END_REF] present a linear regression model by using logarithmic transformation based on the number of views. The authors of [START_REF] Tsagkias | News comments: Exploring, modeling, and online prediction[END_REF] choose to apply regression to predict popularity based on different feature spaces.

In [START_REF] Ahmed | A peek into the future: Predicting the evolution of popularity in user generated content[END_REF], Ahmed et al suggest a predictor based on modeling the transitions that content makes between being a member of different classes of behavior over time. Lee et al. [18] [19] evaluate the probability that a given content will receive more than a given number of hits. Lakkaraju and Ajmera [START_REF] Crane | Robust dynamic classes revealed by measuring the response function of a social system[END_REF] use Support Vector Machines to predict whether a given content will fall in a group that attracts less than 10%, 25%, 50%, 75%, 100% of the attention.

In addition, classification based on the evolution of content popularity shows that there is a small number of temporal patterns [START_REF] Ahmed | A peek into the future: Predicting the evolution of popularity in user generated content[END_REF]. Gursun et al [START_REF] Gursun | Describing and forecasting video access patterns[END_REF] find that there are two types of videos: frequently-accessed and rarely-accessed contents. Frequently-accessed contents are consistently popular over long time periods (e.g: a year). However, rarely-accessed contents show rapid changes in popularity; they are viewed during a small portion of the year.

In [START_REF] Crane | Robust dynamic classes revealed by measuring the response function of a social system[END_REF], Crane and Sornette analyzed the popularity evolution patterns of YouTube contents and identified two main classes: contents experiencing no marked peak in popularity that attract little attention or experience just some popularity fluctuation. This class is called Memoryless. The other class includes contents experiencing bursts in popularity and contains three sub-classes. Viral contents popularity increases slowly, up to a peak, decreasing also slowly afterwards. Quality contents experience a very sudden peak in popularity and a slow decay afterwards. Junk contents know a burst of popularity then their popularity drops quickly afterwards.

III. PROBLEMATIC AND PROPOSED METHODOLOGY

The problem we are interested in is to predict the popularity of video contents retrieved from YouTube. Given a collection of video contents, we study how the popularity of each content evolves since it was uploaded to the YouTube platform till the current time. Based on this evolution description, we are seeking to estimate the popularity of each content in the future. We take into account information available in the YouTube website, (regardless if the content was created or shared somewhere in the network) to observe the number of solicitations of each considered video content during an observation window and predict the number of solicitations.

In this study we use real traces of daily solicitation evolution extracted from YouTube. Let C be the collection of N video contents, and c any video content from this collection. Let E i , i ∈ [1, M ] be the set of experts predicting the future solicitations of each content c. An expert E i is an entity able to analyze an observation window ow i over the past (several consecutive past days) and to predict the solicitation evolution over a prediction window pw i , indeed the next day. We define P S i the prediction strategy of the expert E i . Let y t be the real number of solicitations at time t.

IV. PREDICTION STRATEGIES

We consider different prediction strategies to predict the popularity of contents.

A. Single Exponential Smoothing (SES) prediction

The value p i,t predicted by any Single Exponential Smoothing (SES) [START_REF] Cesa-Bianchi | Prediction, learning, and games[END_REF] expert E i at time t is given by:

p i,t-owi = y t-owi For each k ∈ (t -ow i , t] p i,k = α * y k-1 + (1 -α) * p i,k-1
, where α is a smoothing factor ∈ (0, 1).

B. Double Exponential Smoothing (DES) prediction

Let S i,t denote the single smoothed value obtained by applying SES to y t . S i,t = αy t + (1 -α)S i,t-1 .

Let S i,t denote the double smoothed value obtained by applying SES to S i,t using the same α. S i,t = αS i,t + (1 -α)S i,t-1 , with 0 < α < 1, S i,0 = S i,0 = y 0 . The value predicted by a Double Exponential Smoothing (DES) expert [START_REF] Cesa-Bianchi | Prediction, learning, and games[END_REF] at time t is given by: p i,t+1 = L i,t + T i,t , where L i,t = 2S i,t -S i,t denotes the estimated level and T i,t = α 1-α (S i,t -S i,t ) the estimated trend.

C. Basic expert

We also consider a basic expert E i that at time t > 1 predicts the value p i,t which is equal to the previous value observed y t-1 plus an increment equal to the difference between the two last observed values. Hence, we get:

p i,t = y t-1 + (y t-1 -y t-2 ) = 2y t-1 -y t-2 .
This expert has similarities with a PID controller in control theory [START_REF] Ang | Pid control system analysis, design, and technology[END_REF]. Notice that this expert is very simple and requires no parameter tuning.

D. Error of prediction

We assess the performance of these prediction strategies using the absolute value error function. The relevance of a prediction is measured in terms of instantaneous loss. In this paper, the instantaneous loss is evaluated by the absolute value of the difference between the predicted value and the real one. Hence, at trial t > 0 any expert E i predicting p i,t has an instantaneous loss given by |p i,t -y t |.

E. Improvements of expert predictions

In this section we show how experts improve their prediction when they have additional knowledge about bounds on the values provided by the environment.

Property 1: If ∀t, M in ≤ y t ≤ M ax, with M in and M ax ∈ Z, then any expert E i predicts a value p i,t ∈ [M in, M ax] and has an instantaneous loss |p i,t -y t | ≤ |M ax -M in|.

Proof: Since ∀t, we have M in ≤ y t ≤ M ax, any expert E i will predict a value p i,t that meets M in ≤ p i,t ≤ M ax. More precisely, if the value computed by the expert is smaller than M in, the expert predicts M in. Similarly, if the value computed by the expert is larger than M ax, the expert predicts M ax. Considering these two inequations, we get M in -M ax ≤ p i,t -y t ≤ M ax -M in.

V. PERFORMANCE EVALUATION A. Real traces

For the simulations we use datasheets representing the solicitations of YouTube contents. The trace file associated with each content represents the number of solicitations per day, from the online storage of the video content considered up to the current day. The analyzed traces concern contents belonging to different categories: social, music, sport, news, films, cartoons. The traces present video solicitations during durations varying from 7 months to 5 years. For instance, Figure 1a and Figure 1b depict the total number of solicitations for contents belonging to the category Music during 1878 days, and Society during 534 days, respectively.

B. Use of phases in expert prediction

We analyze different contents with different categories and we notice that contents belonging to the same category has the same appearance of the solicitation curve. Throughout the monitoring duration of each content we observe the existence of periods of consecutive days presenting similar daily increments of the number of solicitations. We denote such period a phase (see for example Figure 1a, where we can distinguish 9 phases in the popularity evolution of the Music video content). The increments of solicitations are very different from one phase to another, determining different slopes on the solicitation curve. We show how to take advantage of these phases to improve the accuracy of expert predictions.

We first define the concepts of best expert on a phase and best global expert. We define E G as the best global expert, that is the expert minimizing the sum of its cumulated losses over all phases. For any phase φ, we define E B(φ) as the best expert on phase φ, that is the expert minimizing its cumulated loss over phase φ.

Property 4: The sum over all phases of the cumulated loss of the best global expert is higher than or equal to the sum over all phases of the cumulated loss of the best expert on each phase.

φ L φ G ≥ φ L φ B(φ)
, where L φ G denotes the cumulated loss over phase φ of E G the best global expert and L φ B(φ) is the cumulated loss over phase φ of the best expert B(φ) on this phase.

Proof: For any phase φ, we have by definition of the best expert on phase φ , L φ i ≥ L φ B(φ) . Applying this inequation to the best global expert E G , we get L φ G ≥ L φ B(φ) . Summing over all phases, we get the property.

C. Tunning of experts parameters

Our first goal is to select the best parameters for each given phase for different content solicitation profiles, and for each expert type. For instance, for SES and DES experts, the parameters to determine are the size of the observation window and the value of alpha. For these values of parameters, the experienced loss should be minimal. Notice that for the basic expert, there is no parameter to tune. SES and DES experts use a smoothing parameter α which varies over time depending on the correlation with the old environment outputs. So, to optimize them, we choose to minimize the cumulated loss between our prediction and the environment output. The optimum value of α at time t is used in the prediction of t+1.

1) SES expert: Figures 2, 3 and 4 depict the cumulated loss for SES experts ignoring the notion of phase, in phase 5 and in phase 6 of the content depicted in Figure 1b, respectively. A small size of the observation window (i.e. ow = 2) is the best, whatever the value of α. A value of α = 0.2 is recommended when the number of solicitations increases very weakly. Otherwise, a value of α close to 1 (i.e. α = 0.9999)) provides the best results, minimizing the cumulated loss.

2) DES expert:

D. Choice of the best expert per phase

We recall that we define the best expert as the expert minimizing its cumulated loss. In this section, we show that Fig. 7: Cumulated loss for DES experts in phase 6 the best expert over all the period predicts worse than the best expert per phase. Fig. 8: DES: cumulated loss on total period vs sum of cumulated loss per phase As expected, Figure 8 shows that real traces confirm Property 4.

E. Comparison between SES, DES and Basic experts

For different contents we compare the performances of the best SES experts, the best DES experts and the basic expert in different phases. The best expert is this minimizing the cumulated loss. Figure 9 clearly shows that the best DES expert outperforms the best SES expert. The cumulated loss of the DES expert is about ten times smaller. Such a result is expected, since DES experts have been designed to take into account the trend in the values observed. Surprisingly, the Basic expert and the best DES expert per phase provide close performances. Simulation results show that Basic is better than DES on 7 phases over 10 phases, but globally the cumulated loss over all phases is smaller for DES. The explanation comes from the sensitivity of the DES expert to small deviations, unlike the Basic expert. More precisely, during phase 7 small deviations on the number of solicitations contribute to increase the instantaneous loss of the DES expert. Hence, the DES expert exhibits a larger cumulated loss. Prediction of the best DES expert per phase and the Basic expert are very close as depicted in Figure 10.

F. Automatic detection of phase changes

Since the instantaneous loss of the Basic expert is usually low, except when the phase changes Figure 11, we decide to use this Basic expert to detect phase changes. Furthermore, this expert adapts faster to phase changes.

We distinguish four types of phase changes, depending on the slope variation of the number of solicitations:

VI. CONCLUSION

We presented a self-learing and prediction method able to predict the number of solicitation individually for each video content in a CDN. The model is based on several experts, each expert having its own prediction strategy (e.g. SES, DES and Basic). The best parameters tunning is determined for each prediction strategy and its accuracy is evaluated. The benefit of using phases during pupularity evolution was proved, a phase being caracterised by a similar slope of the cumulative solicitations evolution curve. Indeed, during one phase one expert can be identified as being more performant to predict then the others. The use of this machine learning method allows the CDN to self-adapt to users solicitations by caching the most popular contents near the end users. More generally, such method can be applied to decide which content should be replicated to improve the performance of video applications and maximize the satisfaction degree of users.

Fig. 1 :

 1 Fig. 1: Cumulated number of solicitations over time.

Figures 5 ,

 5 6 and 7 depict the cumulated loss for DES experts using different sizes of observation window ow i ∈ {2, 3, 4, 5, 6, 7, 8, 9, 10}, expressed in days, where α ∈ [0.7, 0.9999], without considering phase and then in phases 5 and 6 of the content depicted in Figure1b, repectively. Simulations show that values of ow i > 10 and also values of α ∈]0, 0.7] are not significant, the cumulated loss on the analyzed phases being too large.

Fig. 2 :Fig. 4 : 6 Fig. 5 :

 2465 Fig. 2: Cumulated loss for SES experts over all the period

Fig. 9 :

 9 Fig. 9: Cumulated loss for SES, DES and Basic experts.

Fig. 10 :Fig. 11 :

 1011 Fig. 10: Prediction of the best SES, DES and Basic experts.

Fig. 12 :

 12 Fig. 12: Phase changes automatically detected.

  Since both M ax and M in are integers ∈ Z, we finally get |p i,t -y t | ≤ |M ax -M in|. That is the instantaneous loss of expert E i is upper bounded by |M ax -M in|. Property 2: If ∀t, M in ≤ y t ≤ M ax, with M in and M ax ∈ Z, then the expert E i predicting the value p i,t = (M ax -M in)/2 has an instantaneous loss |p i,t -y t | ≤ |M ax -M in|/2. Proof: We notice that ∀t, (M ax -M in)/2 is the median value of [M in, M ax]. Hence, whatever the value we have of t ∈ [M in, M ax], an expert E i predicting a value p i,t = (M ax -M in)/2 has an instantaneous loss |p i,t -y t | ≤ |M ax -M in|/2. Property 3: If ∀t > 0, y t-1 ≤ y t ≤ y t-1 +B, with B ∈ N , then any expert E i predicts a value p i,t ≤ y t-1 + B and has an instantaneous loss |p i,t -y t | ≤ B. Proof: Since ∀t > 0, we have y t-1 ≤ y t ≤ y t-1 +B, any expert E i will predict a value p i,t that meets y t-1 ≤ p i,t ≤ y t-1 +B. Hence, we get by considering these two inequations, -B ≤ p i,t -y t ≤ B. Since B is a natural integer, we finally get |p i,t -y t | ≤ B. That is the instantaneous loss of expert E i is upper bounded by B.

  Detection of a strong increase in the number of solicitations: see for instance time t = 138 on Figure12.a; if l i,t ≥ 2l i,t-1 and l i,t-1 < 2l i,t-2 then there is a phase change at time t with a strong increase.• Detection of a soft increase in the number of solicitations: see for instance time t = 429 on Figure12.b; if l i,t < 2l i,t-1 and l i,t-1 < 2l i,t-2 and l i,t ≥ 1.5l i,t-2 and l i,t-1 < 1.5l i,t-3 then there is a phase change at time t with a soft increase. • Detection of an increase in the number of solicitations smaller than expected: see for instance time t = 184 on Figure12.Detection of an increase in the number of solicitations slightly smaller than expected: see for instance time t = 496 on Figure12.d; if l i,t ≤ 0.7l i,t-1 and l i,t ≤ 0.7l i,t-2 and l i,t > 0.6l i,t-2 then there is a phase change at time t with an increase slightly smaller than expected.

• c; if l i,t ≤ 0.5l i,t-1 and l i,t-1 > 0.5l i,t-2 then there is a phase change at time t with an increase smaller than expected. •

ACKNOWLEDGMENT

This work has been partially funded by the ANR project Netlearn ANR-13-INFR-004.