Marie Balasse
email: marie.balasse@mnhn.fr

Philippe Chemineau

Sara Parisot

Denis Fiorillo

Matthieu Keller

Experimental data from Lacaune and Merino sheep provide new methodological and theoretical grounds to investigate autumn lambing in past husbandries

In temperate Europe, sheep predominantly mate in autumn and lamb in the spring. In contrast, present-day Mediterranean husbandries practice autumn lambing, with benefits in terms of natural resource use and seasonal availability of animal products. Autumnal lambing is enabled by the conjunction of a capability of some Mediterranean breeds for "out-of-season" breeding, intentional scheduling by the herder and autumnal rains providing forage resources for lactation. Autumn and winter sheep births have been demonstrated at Neolithic sites in the western Mediterranean. More works are needed to define the conditions leading to their emergence. This line of research uses oxygen isotope analysis in sheep teeth and involves modern references to define birth season. The existing references were biased in favor of winter and spring births. In this study we enlarge them with 30 additional teeth from Lacaune and Merino sheep, including mainly summer and autumn births.

Experiments were also conducted on Lacaune ewes, to address theoretical grounds on the implementation of autumn births: it implies to preserve females from conceptions by separating the sexes in autumn and reintroducing the rams among females in the spring. This second step also produces a "male effect". We show that in the Lacaune breed, the proportion of spontaneously cyclic ewes in the spring is low in the absence of males and remains minor when the ewes are left in permanent contact with rams. On the other hand, we were able to implement a highly efficient male effect using non-sexually stimulated males, demonstrating that this practice could have been implemented by Neolithic herders.

Keywords (4-6) Sheep, out-of-season breeding, male effect, stable oxygen isotopes, Lacaune, Merino. sheep teeth, in particular Gaëlle Besche for her technical support. We thank two anonymous reviewers for their meaningful comments.

Introduction

Domestication was a major transformation in relationships between humans and animals and also marked the beginning of a whole field of zootechnical knowledge. In particular, domestication induced changes in animals and plants biological rhythms, especially in their reproductive cycle [START_REF] Zeder | Core questions in domestication research[END_REF]. The early history of these evolutionary processes is receiving growing attention from archaeology, as new methodological tools are providing direct evidence for these changes since prehistoric times, and new questions emerge about the environmental and anthropic forces driving them [START_REF] Balasse | Environmental constraints on reproductive activity of domestic sheep and cattle: what latitude for the herder?[END_REF][START_REF] Jones | Population-based resequencing reveals that the flowering time adaptation of cultivated barley originated east of the fertile crescent[END_REF][START_REF] Balasse | Sheep birth distribution in past herds: a review for prehistoric Europe (6 th to 3 rd millennia BC)[END_REF][START_REF] Liu | Journey to the east: Diverse routes and variable flowering times for wheat and barley en route to prehistoric China[END_REF][START_REF] Tornero | Early evidence of sheep lambing de-seasoning in the Western Mediterranean in the sixth millennium BCE[END_REF]. Sheep (Ovis aries L.) is of particular interest in this matter. Sheep lineages initially domesticated in Southeast Anatolia around 8500 BCE were introduced to Europe through Greece and the Balkans in the early 7 th millennium BCE [START_REF] Peters | The upper Euphrates-Tigris basin: Cradle of agropastoralism?[END_REF][START_REF] Zeder | Domestication and early agriculture in the Mediterranean Basin: Origins, diffusion, and impact[END_REF]. From there, they spread both along the northern coastline of the Mediterranean and the Danubian corridor and adjacent rivers to the inland Europe [START_REF] Tresset | Last hunter-gatherers and first farmers of Europe[END_REF]. Along this dispersal across wide longitudinal and latitudinal gradients, sheep were adapted to a diversity of climates and landscapes bearing different constraints on their reproductive cycle in terms of photoperiod and seasonal availability of forages. Under temperate climate, modern sheep have a seasonal breeding activity [START_REF] Hafez | Studies on the breeding season and reproduction of the ewe. Part I. The breeding season in different environments. Part II. The breeding season in one locality[END_REF], based on an endogenous circannual rhythm mainly driven by the photoperiodic cycle via melatonin secretion [START_REF] Karsch | Neuroendocrinal basis of seasonal reproduction[END_REF][START_REF] Malpaux | Control of the circannual rhythm of reproduction by melatonin in the ewe[END_REF][START_REF] Thiéry | Neuroendocrinal interactions and seasonality[END_REF]. This seasonal reproductive activity imposes strong constraints on the socioeconomic livestock systems of farming societies, structuring the agropastoral calendar and determining the availability of animal products during the year [START_REF] Rendu | La montagne d'Enveig. Une estive pyrénéenne dans la longue durée[END_REF][START_REF] Chemineau | Seasonality of reproduction in mammals: intimate regulatory mechanisms and practical implications[END_REF]. Seasonal fertility was inherited from the wild ancestor, the oriental mouflon. Present-day mouflon in the Near East [START_REF] Talibov | Conservation strategy of the asiatic mouflon (Ovis [orientalis] gmelini Blyth) and the Bezoar Goat (Capra aegagrus Erxleben) in Azerbaijan[END_REF] as well as the European mouflon (a feral domestic sheep) found in Corsica [START_REF] Pfeffer | Le Mouflon de Corse (Ovis ammon musimon Schreber 1782); position systématique, écologie et éthologie comparées[END_REF], Cyprus [START_REF] Hadjisterkotis | Reproduction of Cyprus mouflon Ovis gmelini ophion in captivity and in the wild[END_REF] and Sardinia [START_REF] Ciuti | Space use, habitat selection and activity patterns of female Sardinian mouflon (Ovis orientalis musimon) during the lambing season[END_REF] lamb over a short period in the spring. Few data are available for the birthing pattern in early Holocene mouflon as well as in early domestic sheep in southwest Asia. A short lambing period was shown for mouflon during the Late Glacial in Armenia (Tornero et al., 2016a). Pre-Pottery Neolithic sheep at Tell Halula in the Middle Euphrates Valley also show a restricted period of birth [START_REF] Tornero | Seasonal reproductive patterns of early domestic sheep at Tell Halula (PPNB, Middle Euphrates Valley): Evidence from sequential oxygen isotope analyses of tooth enamel[END_REF].

Today in temperate Europe, sheep predominantly mate in autumn to give birth in the spring [START_REF] Hafez | Studies on the breeding season and reproduction of the ewe. Part I. The breeding season in different environments. Part II. The breeding season in one locality[END_REF]. In contrast, in present-day sheep husbandry systems in the Mediterranean area, lambing can also be scheduled in autumn, bringing benefits in terms of natural resource use and seasonal availability of milk and lambs [START_REF] Todaro | Aseasonal sheep and goat milk production in the Mediterranean area: Physiological and technical insights[END_REF]. While occurring only exceptionally in their wild counterparts as well as in sheep husbandries implemented further North, regular autumnal lambing in the Mediterranean area is enabled by the conjunction of three factors: (i) a physiological capability of some Mediterranean breeds for an "out-of-season" breeding, enabling spring mating and autumn lambing; this capacity has a genetic support, as demonstrated by differences between breeds and intra-breed heritability [START_REF] Hanocq | Genetic parameters of spontaneous spring ovulatory activity in Mérinos d'Arles sheep[END_REF][START_REF] Avdi | Genetic variability of spontaneous out-of-season ovulatory activity in Chios sheep[END_REF]; (ii) intentional scheduling by the herder, by separating females and males and reuniting them in the spring [START_REF] Avdi | Reproductive and productive performance in Chios ewes mated in spring or in autumn[END_REF]; this management involving a good understanding of sheep reproductive physiology; (iii) abundant forage resources to support autumn lactation: in present-day Mediterranean climate, autumnal rains create favorable conditions in this regard.

All three conditions may have early met in Neolithic times. Studies involving stable isotope analysis in archaeological sheep teeth highlight variations in the timing of sheep breeding through time (6 th -3 rd mil. BCE) and space along the Neolithic dispersal routes: spring lambing was demonstrated at middle-latitude sites in Europe (42°-46°N) while a later onset of the breeding season at higher-latitudes sites (59°N) is explained by different photoperiodic conditions [START_REF] Balasse | Sheep birth distribution in past herds: a review for prehistoric Europe (6 th to 3 rd millennia BC)[END_REF][START_REF] Balasse | Neolithic sheep birth distribution: Results from Nova Nadezhda (sixth millennium BC, Bulgaria) and a reassessment of European data with a new modern reference set including upper and lower molars[END_REF]. In sharp contrast to this pattern, predominant autumn and winter sheep births are attested at early and middle Neolithic sites in southern France and the Iberian Peninsula [START_REF] Tornero | Early evidence of sheep lambing de-seasoning in the Western Mediterranean in the sixth millennium BCE[END_REF][START_REF] Sierra | Sheep husbandry in the early Neolithic of the Pyrenees: new data on feeding and reproduction in the cave of Chaves[END_REF][START_REF] Fabre | Nouvel éclairage sur les systèmes d'élevage ovins du Chasséen. Reproduction, alimentation et productions animales à Auriac, Carcassonne[END_REF]. Autumn births were also reported at Bronze and Iron Age sites in Central Asia (Kazakhstan;[START_REF] Ventresca Miller | Close management of sheep in ancient Central Asia: evidence for foddering, transhumance, and extended lambing seasons during the Bronze and Iron Ages[END_REF][START_REF] Hermes | Carbon and oxygen stable isotopic evidence for diverse sheep and goat husbandry strategies amid a Final Bronze Age farming milieu in the Kyrgyz Tian Shan[END_REF] and at Late Bronze Age sites in the South Caucasus [START_REF] Chazin | Multi-season reproduction and pastoralist production strategies: new approaches to birth seasonality from the South Caucasus region[END_REF], although current data sets indicate low occurrence. In our opinion, this low occurrence does not reflect the herders' strategy towards autumnal lambing.

Interestingly, sites in Thrace and the Lower Danube from the earliest Neolithic cultures in Europe show a spring lambing pattern [START_REF] Balasse | Neolithic sheep birth distribution: Results from Nova Nadezhda (sixth millennium BC, Bulgaria) and a reassessment of European data with a new modern reference set including upper and lower molars[END_REF] despite their location at comparable latitudes to those in the Northwestern Mediterranean showing autumn lambing. This suggests that additionally to photoperiod, other factors have been determinant, including climate, farmers' technicity and socio-economic systems. Current sheep husbandries across the northern Mediterranean basin show great variety in their forms and goals. Autumnal lambing is not an exclusive practice, depending on multiple factors including the orientation of production, forage resources and seasonal mobility [START_REF] Brooke | Races ovines méditerranéennes en régression[END_REF]. Autumnal lambing systems are therefore a demonstrative example of close interconnections between biology, environment and technical systems. More extensive systematic research is needed to define more precisely the conditions that led to their emergence in the Mediterranean area. The production of additional zooarchaeological datasets must also be accompanied by a strengthening of the methodological and theoretical grounds supporting this research.

On a methodological level first, sheep birth seasonality is investigated through the reconstruction of the seasonal cycle record in tooth, from sequential analysis of enamel stable oxygen isotope ratios (δ 18 O). As the teeth growth timing is fixed within species, the season of birth determines the sequence of the seasonal cycle recorded in a given tooth. Interindividual variability in this record reflects births seasonality (Bryant et al., 1996a&b;[START_REF] Balasse | Determining sheep birth seasonality by analysis of tooth enamel oxygen isotope ratios: the Late Stone Age site of Kasteelberg (South Africa)[END_REF]. Depending on the best represented tooth in the assemblage, the analysis is conducted on the second (M2) or the third molar (M3). The season of birth is determined through comparison with reference data obtained from modern sheep whose season of birth is known (Balasse et al., 2012). Currently used modern reference sets are globally biased towards late winter and spring births -the currently dominant lambing season in temperate Europe (Blaise & Balasse, 2011;Balasse et al., 2012;[START_REF] Tornero | The altitudinal mobility of wild sheep at the Epigravettian site of Kalavan 1 (Lesser Caucasus, Armenia): Evidence from a sequential isotopic analysis in tooth enamel[END_REF][START_REF] Balasse | Neolithic sheep birth distribution: Results from Nova Nadezhda (sixth millennium BC, Bulgaria) and a reassessment of European data with a new modern reference set including upper and lower molars[END_REF]. As a result, from isotope analyses performed in third molars, autumn lambing can only be identified as births occurring in the opposite season to spring (Hadjikoumis et al., 2018;[START_REF] Fabre | Nouvel éclairage sur les systèmes d'élevage ovins du Chasséen. Reproduction, alimentation et productions animales à Auriac, Carcassonne[END_REF]. These modern reference sets must also be enlarged in number and include a higher diversity of birth seasons and sheep breeds, to challenge the time resolution of the approach and comparability between breeds. The need to expand reference sets is particularly true for the third molar, on which they are currently very scarce [START_REF] Balasse | Neolithic sheep birth distribution: Results from Nova Nadezhda (sixth millennium BC, Bulgaria) and a reassessment of European data with a new modern reference set including upper and lower molars[END_REF]. Although a less regular ontogenic scheduling has been observed for the M3 compared to the M2 [START_REF] Zazzo | The isotope record of short-and long-term dietary changes in sheep tooth enamel: Implications for quantitative reconstruction of paleodiets[END_REF], focusing on the M3 is also legitimate because of the need to secure tooth identification in assemblages mostly composed of isolated teeth, where second and first molars may be mixed up. Furthermore, depending on demographic management linked to the orientation of production, younger age classes may be poorly represented and in that case the crowns of the second molars will be heavily worn and the study will be conducted preferentially on the third molars.

On a theoretical level then, present day European sheep breeds are short-day breeders: the fertility period starts in autumn and lambing occurs predominantly in late winter/spring after a five-month gestation.

Predominant autumn births within a flock can only be achieved by the voluntary manipulation of reproduction by the farmer in two successive steps. The first one is to preserve females from conceptions by separating the sexes in autumn in order to have them ready to be pregnant the next spring. Then, the second step is to reintroduce the rams among females in the spring to hope to have a maximum number of out-of-season pregnancies. The success of this second step is dependent on the ability of the breed for out-of-season mating and the intensity of sexual activity of males which produce a "male effect" by reactivating ovulations and heats in the females in sexual rest under a precise time course (Girard, 1813, Véliz et al., 2002[START_REF] Chasles | Sexually active bucks are efficient to stimulate female ovulatory activity during the anestrus season also under temperate latitudes[END_REF].

The question remains as to the extent to which prehistoric breeders could have used these two steps of separation of sexes in autumn followed by a male effect to produce autumn lambing.

Both these methodological and theoretical points were addressed in this study. Third molars were collected from Lacaune and Merino d'Arles sheep in order to extend the oxygen isotope reference data used to determine birth season. Experiments were conducted on Lacaune ewes to quantify the relative proportion of females spontaneously ovulating in the spring, with or without the presence of males, and the effectiveness of a male effect in terms of ovulation using non-sexually stimulated males. Indeed, sexual stimulation currently involves hormonal (melatonin) or light treatments, which were only developed within the last decades and were therefore not within the reach of the Neolithic herders.

Material and methods

Stable isotope reference set for birth season

The currently used modern reference sets (Table 1) are composed of sheep teeth from diverse locations including Rousay in Orkney islands (Balasse et al., 2012), Carmejane in southern France (Blaise & Balasse, 2011;Tornero et al., 2013), Selgua in north-eastern Spain [START_REF] Tornero | The altitudinal mobility of wild sheep at the Epigravettian site of Kalavan 1 (Lesser Caucasus, Armenia): Evidence from a sequential isotopic analysis in tooth enamel[END_REF] and Kemenez in French Brittany [START_REF] Balasse | Neolithic sheep birth distribution: Results from Nova Nadezhda (sixth millennium BC, Bulgaria) and a reassessment of European data with a new modern reference set including upper and lower molars[END_REF]. They include sheep from different breeds (Shetland cross, Ouessant x Lande de Bretagne, Préalpes du Sud, Xisqueta) born in late winter and spring for the majority, or in early autumn for very few of them. The bias towards late winter/spring births is particularly true for the third molar (M3) with only one representative of an autumn birth in the Kemenez reference set [START_REF] Balasse | Neolithic sheep birth distribution: Results from Nova Nadezhda (sixth millennium BC, Bulgaria) and a reassessment of European data with a new modern reference set including upper and lower molars[END_REF]. In this study, we extend these modern references with sheep of the Lacaune and Merino d'Arles breeds, born in various seasons, with an emphasis on autumn births (September to December). The study material includes the molars from 21 sheep from the Lacaune breed and nine sheep from the Merino d'Arles breed (Online Resource 1). The Lacaune sheep come from seven different farms in southern France (Aveyron). They constitute four groups born in summer ( 26July -11 August, N=5), early autumn (15 -23 October, N=8), late autumn (1 -5 December, N=6) and early winter (1 & 10 January, N=2) in different years (2013)(2014)(2015)(2016). The Merino d'Arles sheep come from an experimental farm in southern France (Domaine du Merle, Salon de Provence) and were born in late summer/early autumn (12 September -10 October) or winter/early spring (25 February -7 April). All sheep were females aged between 2.5 and 5 years at time of slaughter (except one aged 6.5 years). This age class was targeted to provide third molars with fully developed crowns and limited tooth wear, more likely to deliver a complete record of an annual cycle. The third molars were extracted from mandibular bones and cleaned by boiling. Sequential sampling of enamel was performed by drilling series of bands perpendicular to the tooth growth axis, on the second lobe of the molar, on the vestibular side. Each sample is located in tooth crown using its distance from the enamel-root junction (erj) [START_REF] Balasse | Determining sheep birth seasonality by analysis of tooth enamel oxygen isotope ratios: the Late Stone Age site of Kasteelberg (South Africa)[END_REF]. The stable oxygen isotope ratios (δ 18 O) were measured on the carbonate fraction of enamel bioapatite. Enamel samples weighing ~600 µg were reacted with 100% phosphoric acid at 70°C in individual vessels in an automated cryogenic distillation system (Kiel IV device), interfaced with a DeltaVAdvantage isotope ratio mass spectrometer. The analytical precision for each run, estimated from 6 to 8 analyses of our laboratory carbonate standard (Marbre LM, expected value -1.83‰ calibrated to the NBS 19 international standard) is lower than 0.05 ‰.

The retrieved intra-tooth sequences of stable oxygen isotope ratios reflect the recording of the seasonal cycle during tooth crown formation (Bryant et al., 1996a&b), spanning approximately a year in the sheep third molar [START_REF] Weinreb | Tooth development in sheep[END_REF][START_REF] Milhaud | Développement des molaires chez le mouton. Etude morphologique, radiographique et microdurométrique[END_REF]. Stable oxygen isotope ratios in the mineral fraction of animal skeletons linearly correlate to the stable oxygen isotope composition of local annual precipitation [START_REF] Land | Isotopic ecology of deer bones[END_REF][START_REF] D'angela | Oxygen isotopes in living mammal's bone phosphate: further results[END_REF]. In continental Europe, the precipitation δ 18 O values are affected by seasonal variations in air temperature, resulting in cyclical variations on an annual scale [START_REF] Rozanski | Isotopic patterns in modern global precipitation[END_REF].

Additionally, a significant part of seasonal variation in body water oxygen isotope composition results from animal behaviour and physiology in response to changes in temperature and air humidity [START_REF] Chen | Model explanation of the seasonal variation of δ 18 O in cow (Bos taurus) hair under temperate conditions[END_REF]. All factors combine to create a seasonal signal in tooth enamel δ 18 O values. As the tooth growth timing is fixed within species, the season of birth determines the sequence of the annual cycle recorded in a given tooth.

The δ 18 O sequences measured in the sheep M3 were modelled using an equation derived from a cosine function (the procedure is described in Balasse et al., 2012; see also Online Resource 2). The model defines the amplitude (A) and the mean (M) of the signal, as well as the position (x0) of the maximum δ 18 O value and the period of the cycle (X, distance over which the isotopic record covers one annual cycle). The latter is used to normalize the distances in order to eliminate inter-individual variability in tooth size. The resulting x0/X ratio for each specimen is a reference value for the specimen's birth date. In addition to the δ 18 O sequences obtained from the Lacaune and Merinos sheep molars, the previously published sequences from four North-Ronaldsay sheep born in April/May [START_REF] Balasse | The use of isotope ratios to test for seaweed eating in sheep[END_REF] were also modelled. The x0/X ratios are reported on circular charts reflecting the cyclical nature of seasonality [START_REF] Balasse | Neolithic sheep birth distribution: Results from Nova Nadezhda (sixth millennium BC, Bulgaria) and a reassessment of European data with a new modern reference set including upper and lower molars[END_REF]; see Online Resource 2 for the construction of this chart). All calculations have been carried out using the Microsoft Excel software. The fitting of the model to the dataset is estimated using the Pearson correlation coefficient (r) (Pearson function in the Excel software). We consider that the model describes adequately the dataset when r≥0.91.

Ram effect experimental design

The experiments were conducted on Lacaune dairy sheep raised at the INRAE La Fage experimental domain (Aveyron, southern France). The Lacaune breed is a local breed whose place of origin is the southern Massif

Central. The breed selection for characteristics linked to dairy production (milk quantity and richness, udder morphology), was done in Lacaune pure breed, only began recently (less than 50 years ago) and did not involve introgression of foreign genes [START_REF] Barillet | Objectifs de sélection et stratégie raisonnée de mise en oeuvre à l'échelle des populations de brebis laitières françaises[END_REF]. The Lacaune dairy breed has never been selected on the ability for out-of-season lambing.

Experiment 1

The objective was to (i) determine whether Lacaune ewes in the continuous presence of rams (PR) ovulate spontaneously in the spring and, if so, in what proportions;

(2) measure the effectiveness of a "ram effect" (RE) in spring in terms of ovulation, without previous stimulation of the ram (i.e. without artificial excitation of sexual activity). Two groups of 20 ewes each were constituted on February 17, 2020 (day 0). The groups were balanced in age and weight and all were non-lactating ewes (Online Resource 3). The two groups were kept separately in different sheepfolds. In group PR (Presence of Ram), two rams were introduced on day 0 and were kept permanently with the ewes until the end of the experiment. In group RE (Ram Effect), the ewes were kept separated from rams until two rams were introduced into the group on May 18, 2020. Blood samples were taken from the jugular vein from May 11, twice a week until June 19 when the experiment finished.

Experiment 2

The relative proportion of ewes ovulating spontaneously in spring was determined in a sample of 100 lactating ewes. The group, which was representative of the flock, was composed of 31 ewes in first lactation (L1), 25 in L2, 14 in L3 and 30 in L4 or more. They were herded normally with the rest of the flock (450 ewes, i.e. 550 in total) and kept separated from rams. Blood samples were taken from the jugular vein on May 3, May 6 and May 10, 2021.

In both experiments, ovulations were detected by measuring plasma progesterone (P4) concentrations. Blood samples were obtained by jugular venipuncture in 5 mL tubes containing heparin. Plasma was obtained after 30 min of centrifugation at 3,500 × g and concentration of plasma progesterone was determined in samples using an immunoenzymatic assay as described previously [START_REF] Canépa | Validation d'une méthode immunoenzymatique pour le dosage de la progestérone dans le plasma des ovins et des bovins[END_REF]. Sensitivity of this assay was 0.25 ng/mL. The mean intra-assay and inter-assay coefficients of variation were <10%. Females with progesterone concentrations ≥1.0 ng/mL samples were considered to have ovulated [START_REF] Thimonier | Progesterone level analysis for the determination of the physiological status of female farm animals[END_REF].

Results from stable isotope analysis of sheep enamel

Results from the sequential analysis of enamel stable oxygen isotope ratios and the modeling of the Among the Lacaune sheep, the mean x0/X ratios for each birth group follow each other according to their respective place in the calendar cycle (Table 2). Within each birth group, the (x0/X) ratios do not always rank according to the date of birth. Moreover, the reconstructed birth interval (in days) within each group is always higher than the real birth interval: although the Lacaune summer (July-August), early autumn (October) and late autumn (December) sheep were born respectively over 16, 10 and 5 days (in different years), the reconstructed birth interval is respectively 51, 53 and 57 days (Table 2). The x0/X ratios of the Lacaune sheep born in October largely overlap with those born in August, and partially with those born in December (Figure 3a). The x0/X ratios obtained from the Merino sheep divide into two groups (Figure 3b): in agreement with the pool of birth dates associated with these mandibles and from comparison with pre-existing references, six are attributed to September/October births and two to winter/early spring births. The mean x0/X ratio measured for the Merino sheep born in Sept/Oct (0.69) is similar to the one measured for the Lacaune sheep born in October (0.67). Fig. 1 Results from sequential analysis of stable oxygen isotope ratios in the Lacaune sheep tooth enamel.

The sequences that could not be modelled are not included in this figure

Results from the ram effect experiment on Lacaune ewes

Results from the ram effect experiment are given in Online Resource 3, Table 3 andFigure 4. In both experiments the percentage of spontaneously cycling ewes without ram is between 16 and 25% and there is no difference between groups 2020-RE (before ram effect) and 2021-NR. In 2020 in non-lactating ewes, only 5 out of 20 ewes cycled in the group isolated from rams and 6 out of 20 cycled in the group in permanent presence of rams. In 2021, among 100 lactating ewes maintained without rams, only 16 cycled.

In the 2020-RE group, the sudden introduction of rams in 2020 produced a dramatic increase in the number of ewes ovulating and this group of ewes showed 100% of females cycling afterwards. At reverse, over the same period, in the 2020-PR group maintained in the permanent presence of rams only 2 more ewes cycled.

Discussion

Interindividual variability in the recording of the δ 18 O sequences Birth intervals appearing larger than they actually are, and the overlap in data between different birth groups are mostly due to inter-individual variability in the timing of tooth development: the sequence of the seasonal cycle recorded in a given tooth depends on when, during the annual cycle, the record began, i.e. the date of birth (which we are trying to reconstruct) and the age at which the tooth began to form. The normalization procedure using the period of the cycle (X) eliminates variability in tooth size, not variability in the timing of tooth development. The latter has not been quantified in sheep molars, and the absence of a significant effect of sex, nutritional regime and breeding age in cheek teeth eruption [START_REF] Worley | The Sheep Project (2): The effects of plane of nutrition, castration and the timing of first breeding in ewes on dental eruption and wear in unimproved Shetland sheep[END_REF] does not mean the absence of inter-individual variability. From the results obtained in the Lacaune ewes born within five days in December, it appears that inter-individual variability in the timing of development of the third molar would have be approximately 1.5 months in this group. This methodological barrier must be taken into account when interpreting archaeological data sets.

Comparison with preexisting reference sets for sheep birth season

This new dataset from Lacaune and Merino sheep is combined to previous reference sets in Figure 5. There is a good coherence between all reference sets in spite of the use of different sheep breeds, suggesting that interbreed variability in the timing of tooth development does not create significant additional imprecision for the determination of birth season. In the present state, this composite reference set allows to distinguish winter from spring births (notwithstanding a small overlap), and to distinguish both from mid-summer and autumn births. However, in the present state it is not possible to distinguish mid-summer births from early autumn births (Figure 5).

It should also be noted that different degrees of certainty are attached to these different reference sets. The highest degree of certainty may be given to the Lacaune reference sheep teeth, which all come from identified individuals with known birth dates. The Merino sheep from Le Merle, disconnected from their identification buckles, were provided with birth dates grouped in two lots (winter and early spring, or autumn) that were far enough apart in the annual cycle to be clearly identified from the results of the analyses (Figure 3b). Even though interindividual variability in the timing of tooth growth is a source of uncertainty, we consider it highly unlikely that it will lead to the misattribution of a winter/early spring birth to an autumn birth -and vice versa; nevertheless, within each births group the sheep cannot be attributed to a date of even a month of birth. The Kemenez reference set [START_REF] Balasse | Neolithic sheep birth distribution: Results from Nova Nadezhda (sixth millennium BC, Bulgaria) and a reassessment of European data with a new modern reference set including upper and lower molars[END_REF] is composed of teeth collected on the Kemenez island. They all come from a unique flock for which sheep births had been precisely referenced over seven previous years (2008-2013 and 2015, N=255), with almost all births occurring between mid-January and mid-April (94%), a marked lambing peak (73%) in February and until mid-March, and rare births in May/June, August and October. The results could be compared to the known distribution of births. Most of them almost certainly belong to mid-January to mid-April and most likely to February until mid-March. The attribution of two of them to respectively May/June and October has a lower degree of certainty. Last, the North-Ronaldsay reference set [START_REF] Balasse | The use of isotope ratios to test for seaweed eating in sheep[END_REF] includes mandibles collected from skeletons on the shore of North-Ronaldsay island. They derive from the collectively managed flock, in which lambing occurs mostly in April and May, but the precise birth dates were not known. Despite these uncertainties of varying degrees, the current paucity of modern references for δ 18 O sequences lead us not to eliminate them but to consider each of them with the necessary caution, until additional data are produced. Our experiment has shown that without manipulation of socio-sexual relations within the herd, the proportion of spontaneously cyclic ewes in the spring is low (16% in lactating females, 25% in non-lactating females) when males are absent, even in a breed with a high capacity for out-of-season breeding such as the Lacaune. The proportion of spontaneously cyclic ewes in the spring tended to be higher (40% vs 16%, table 3, last column) when the ewes were left in contact with the rams. However, currently in a seasonal system where rams are kept permanently with the ewes with no manipulation by the herder, lambs are born in late winter (February). They reach puberty and are fertilized in mid-autumn or winter (November-December) if their growth rate is sufficient, then lamb in March-April. After a lactation of at least three months they are fertilized with adults in the next autumn (September) to lamb in February. Ewe lambs that were not fertilized in their first year (if feeding conditions during growth were poor) and ewes that have lost their lamb and stopped nursing, can escape to this scheme and be fertilized in the spring to give birth in autumn. Those do not predominate in the flock but can represent a few tenth of percent (10-20%). In such a system, autumn births could indeed occur, but they will be few [START_REF] Mauléon | Variations de durée de l'anoestrus de lactation chez les brebis de race Ile-de-France[END_REF][START_REF] Perret | Races ovines[END_REF].

We have shown that a ram effect could be performed in the Lacaune breed using non-sexually stimulated males, and that in such case, the ram effect is highly efficient (100% of females ovulating after the ram effect).

These results, as well as many others already published [START_REF] Martin | The physiological-responses of anovulatory ewes to the introduction of rams -A review[END_REF], demonstrate that the ram effect is a simple and efficient way to obtain a majority of births in autumn, even though many other factors affect the outcome of ovulations into lambings. It must be noted, that when separating and then joining again both sexes, a ram effect is implemented, whether intentionally by the herder to produce induced ovulation among ewes, or not just by joining rams and ewes. In an out-of-season system, the herder must then decide when and how he would start the "deseasoning" in his flock: (a) one possibility is to shift lambing time starting with the ewe lambs by delaying their fertilizations until when they are approximately 15 months old (in May, if born in February), then once adults, the ewes will always be fertilized in May and give birth in October to ewe lambs that will mate in the following May; (b) another possibility is to shift lambing time in adults by delaying the September mating to the following May. In both cases (a and b), it is necessary to separate rams from ewes at some point and for some time, and when the herder puts the males back with the females in the spring, there is a ram effect, even though perhaps unintentional. The two systems (a and b) are quite subtle and undoubtedly risky if herd management (feeding conditions and separation of sexes) is not well conducted, and cannot be easily conceivable in situations where flocks are at pasture and mixed with others at certain periods (estivation). In such a system, autumn births can predominate if the management is successful, or only reach around 60% if management fails. In the latter case, if spring fertility is low, the herder must set up autumn mating as a "catchup" mating, with the problems that this entails, notably spring births and the difficulty of putting these ewes back into the spring mating scheme afterwards.

Conclusions and perspectives

The results from the present study double the currently available reference data for sheep birth season inferred from δ 18 O sequences in the third molar. They provide the first robust reference set for late summer and autumn births. Interindividual variability in the timing of the third molar growth has been shown to induce imprecision in the determination of birth date. If interindividual variability was similar in ancient sheep, this may also affect the determination of the duration of the lambing period. The new reference sets from Lacaune and Merino ewes combine well with previous ones obtained in other sheep breeds, suggesting that interbreed variability in the timing of tooth growth does not create significant additional imprecision. In the present state, it is unrealistic to try and determine sheep birth season on a monthly scale. In spite of these restrictions, some of which could be addressed with a statistical approach when the data is enlarged, we can confirm that spring lambing, resulting from a reproduction cycle driven mainly by the photoperiodic cycle (that is, environmental factors), can be clearly distinguished from autumn lambing, involving manipulation of ewe reproductive cycle by the herders. This question would be the subject of major interest at the moment, illustrating complex interactions between animal physiology, environmental constraints and technical systems.

Concerning herd management, this study has shown, on the one hand, that in the Lacaune breed with a high capacity for out-of-season breeding, the proportion of spontaneously cyclic ewes in the spring is low in the absence of males, and remains minor when the ewes are left in permanent contact with rams. On the other hand, we were able to implement a highly efficient male effect using non-sexually stimulated males, demonstrating that this practice could have been implemented by Neolithic herders, even if we do not know if ancient ewes had the same responsiveness as the modern ones. The occurrence of predominant autumn births in a flock necessarily means a capacity for out-of-season breeding in the ovine population as well as a manipulation of reproduction involving the separation of both sexes in the autumn followed by their reuniting in the spring, thus achieving a male effect, whether intentionally or not. The interpretation of archaeological data in terms of reproduction management lies on the estimation of the relative proportion of autumn births, as autumn birth may also occur, without a manipulation by the herder but only to a small proportion. Larger archaeological datasets must be produced to achieve this goal, and combining data obtained from the second and third molars must be considered in the future, now that we have modern references for both teeth.

  sequences are extensively reported in Online Resource 2. A large majority of δ 18 O sequences show the expected pattern of cyclical variation reflecting the seasonal pattern (Figures 1 & 2). Four of the 21 sequences obtained from the Lacaune sheep molars (MUT 161641-40131, MUT 161641-50136, MUT 161641-6119, MUT 161345-50393) and one of the nine sequences obtained from the Merino sheep (MRL 84379) gave non-sinusoidal, strongly asymmetric, or incomplete annual δ 18 O sequences, and for this reason could not be modelled using the equation derived from a cosine function.

Fig. 2 Fig. 3

 23 Fig.2 Results from sequential analysis of stable oxygen isotope ratios in the Merino sheep tooth enamel. The purple sequences are attributed to the autumn births group (September or October); the yellow sequences to the winter/early spring births group (late February, March, or early April)

Fig. 4

 4 Fig.4 a-Percentage of cycling ewes in each experimental set. PR = presence of ram; RE: ram effect; NR: no ram. b-Examples of variations in the concentration of plasma progesterone (P4) over the course of the experiment. The red dotted line sets the minimum progesterone concentration (1.0 ng/mL) at which ewes were considered to have ovulated. The black arrow indicates the date of introduction of the ram in the RE group. The shaded area indicates when the rams were present in the groups

Fig. 5

 5 Fig.5 Circular charts showing the distribution of x0/X ratios in all reference sheep: a -according to the breed and birth month: Ouessant x Landes de Bretagne (Kemenez; Balasse et al., 2020), North-Ronaldsay (Balasse et al., 2005), Lacaune (La Fage, this study) and Merino (Le Merle, this study). Monthly grouping; b -Seasonal grouping

Table 1 :

 1 Stable isotope reference sets for sheep birth season. References: 1 -Balasse et al. (2012); 2 -Blaise & Balasse (2011); 3 -Tornero et al. (2013); 4 -Tornero et al. (2016); 5 -Balasse et al. (2020); 6 -Balasse et al. (2005).

	Name	Sheep breed	Tooth	Birth months	Reference
	Rousay (ROU)	Shetland cross	lower M2 (N=10)	Apr/May	1
	Carmejane (CAR)	Préalpes du Sud	lower M2 (N= 5)	Jan, Fev, Sept	2 and 3
	Selgua (XT)	Xisqueta	lower M2 (N=2)	October	4
	Kemenez (KMZ)	Ouessant x Lande de Bretagne	lower M2 (N=4)	Jan-March	5
	Kemenez (KMZ)	Ouessant x Lande de Bretagne	lower M3 (N=16)	Jan-Mar, May/Jun, Oct	5
	Kemenez (KMZ)	Ouessant x Lande de Bretagne	upper M3 (N=8)	Jan-March, Oct	5
	North-Ronaldsay (NR)	North-Ronaldsay	lower M3 (N=4)	April/May	6
	Le Merle (MRL)	Merino d'Arles	lower M3 (N=9)	Feb/Mar/Apr, Sept/Oct	This study
	La Fage (MUT)	Lacaune	lower M3 (N=17)	Jan, Jul, Aug, Oct, Dec	This study

The Lacaune and Merino sheep mandibles were recovered from the slaughterhouse with the sheep's identification buckles. The Merino sheep mandibles were dissociated from their respective buckles during processing at the slaughterhouse. For this reason, the sheep can be attributed to a group born between late February and early April, or a group born in September/October but identification at the individual level could not be done (see Results and Discussion).

Table 2 :

 2 Mean and range of x0/X ratios measured in the different birth groups in the Lacaune sheep (D = birth interval). Individual data are given in Online Resource 2.

	Reference

sheep Birth group (N) Dates Real D (days) x0/X (mean) x0/X (range) Reconstructed D (days)

	Lacaune	January (1)	10 Jan	/	0.05	/	/
		July-August (5)	26 Jul -11 Aug	16	0.62	0.14	51
		October (5)	15-23 Oct	10	0.67	0.15	53
		December (N=6)	01-05 Dec	5	0.83	0.13	47

Table 3 :

 3 Number of spontaneously cycling ewes, not cycling ewes, and cycling ewes after ram introduction, in each experimental set.

	N ewes Spont. cycling Non cycling Cycling ewes after N cycling ewes
		ewes	ewes	ram introduction (total period)
	2020 -RE (ram effect) 20	5	15	15	20
	2020 -PR (presence of ram) 20	6	14	8	8
	Fisher's Exact Test	NS		P<0.01	P<0.01
	2021 -NR (no ram) 100	16	84	/	16

Acknowledgements

We would like to thank David Portes and Charlotte Allain (INRAE La Fage experimental unit) for taking blood samples on the Lacaune sheep, the INRAE hormone assay laboratory at Tours-Nouzilly. The Lacaune sheep mandibles were provided by the Confédération Générale de Roquefort-Service élevage; we thank the butchers at the Theix INRAE center for the Lacaune sheep mandibles treatment. The Domaine du Merle experimental farm is part of Montpellier SupAgro. We thank Pierre-Marie Bousquet and his team for providing us the Merino

This project has received financial support from the INRAE and the CNRS through the MITI interdisciplinary programs ("AgroPaléoRepro" project, 2019("AgroPaléoRepro" project, -2020)). The experiment on the Lacaune sheep received approval by the ethics committee on animal experimentation, science and health (SSA), n°115. The decision to authorize the project is referenced as APAFIS#22807-2019110814002486.


M Georgiou

G Mercier

D Mounié

Towards Container Trystram

Experimental Protocol

Adaptation of the benchmark FunctionBench ¹, Deployment of OpenWhisk ² on GRID5000 ³, Measurement and calibration of results.

Evaluation of scheduling policies FOA, K8S ImageLocality (baseline):

In a simulated environment, On top of Batsim/ Simgrid [H.Casanova et.al, 2014].

¹ https://github.com/kmu-bigdata/serverless-faas-workbench , ² https://openwhisk.apache.org/, ³ https://www.grid5000.fr . Environment id of the j-th function x ij Placement of the j-th function on the i-th machine e ik Placement of the k-th environment on the i-th machine 3) The dependency between functions and environments is known.

Parameters

FOA's Linear Program

The Linear Program minimizes the cost under a makespan constraint of value T

Min M i=1 N j=1 c ij × x ij + M i=1 K k=1 d ik × e ik (1) ∀i ≤ M, N j=1 p ij × x ij + K k=1 b ik × e ik ≤ T (2) ∀j ≤ N, M i=1 x ij ≥ 1 (3) ∀i ≤ M, ∀j ≤ N, x ij ≤ e i,env [j] (4) ∀i ≤ M, ∀k ≤ K , N j=1 x[i][j] ≤ N ik × e[i][k] (5) ∀i ≤ M, ∀k ≤ K , e ik ≤ 1 (

  functions K Number of container environments c ij Cost of the j-th function on the i-th machine p ij Execution time of the j-th function on the i-th machine d ik Cost of the k-th environment on the i-th machine b ik Execution time of the k-th environment on i-th machine env [j]

Figure 10 :

 10 Figure10: The makespan (y-axis) against the number of machines used (x-axis).

Table 1

 1 Design of Experiments. Total of 1620 experiments.

		Values
	Workload Size	200, 600, 1000
	Platform Size	100, 300, 500
	Heterogeneity Level	3, 5, 7
	Scheduling Policies	FOA, K8S ImageLocality
	Random Seeds	30

Anderson Andrei DA SILVA, Y. Georgiou, M. Mercier, G. Mounié, D. Trystram Towards Container-layer-aware Scheduling Policy for Serverless-based Edge-Cloud Continuum

Table 1

 1 Design of Experiments. Total of 1620 experiments.

	Function	Input Values	Unit
	Chameleon	2.10 3 , 3.10 3	Matrix size
	Float operation	10.10 7 , 20.10 7 , 30.10 7	Operations
	Image processing	60, 40	Image size in MB
	Linpack	5.10 3 , 6.10 3	Matrix size
	Matrix Multiplication	3.10 3 , 4.10 3	Matrix size
	Model Training	50, 100	Dataset size
	Pyaes	3.10 3 , 4.10 3 , 5.10 3	Length of message
	Video Processing	30, 50, 100	Video size in MB

Table 2 :

 2 Functions adapted from FunctionBench.

, Platform, Containers usage Outputs Batsim Anderson

	Simulation infrastructure
	Batsim Inputs
		Workload		Platform	Scheduling	Main
	x	y	z	w	Description	Policy	Components
	Workload -Profiles	Profiles -Containers
		Associations		Associations
	Workload Profiles {x} {y} {z} {w}	a d h {x} {y} a c g	b f i {z} {w} a e h	Extra Layers
					Container Layers
						Batsim Inputs Communication
		Simulation Infrastructure		SimGrid
					Batsim Outputs
			Scheduling
								Cloud Continuum	13 / 35

Anderson Andrei DA SILVA, Y. Georgiou, M. Mercier, G. Mounié, D. Trystram Towards Container-layer-aware Scheduling Policy for Serverless-based Edge-Andrei DA SILVA, Y. Georgiou, M. Mercier, G. Mounié, D. Trystram Towards Container-layer-aware Scheduling Policy for Serverless-based Edge-Cloud Continuum

Table 1 :

 1 FOA's list of notation and descriptions.

	Assumptions:
	1) Functions and
	environments are
	independent and known
	in advance;
	2) Their cost and
	processing time on each
	machine are known;

Anderson Andrei DA SILVA, Y. Georgiou, M. Mercier, G. Mounié, D. Trystram Towards Container-layer-aware Scheduling Policy for Serverless-based Edge-Cloud Continuum

The Minimum Cost Integral Matching phase uses the Dual-Approx. Algorithm of Shmoys and Tardos [D. B. Shmoys and E. Tardos, "An approximation algorithm for the generalized assignment problem," Math. Program., vol. 62, no. 1-3, p.461-474, Feb. 1993]. Anderson Andrei DA SILVA, Y. Georgiou, M. Mercier, G. Mounié, D. Trystram Towards Container-layer-aware Scheduling Policy for Serverless-based Edge-Cloud Continuum

Anderson Andrei DA SILVA, Y. Georgiou, M. Mercier, G. Mounié, D. Trystram

Conclusions -Part 1

Cloud greedy algorithms may not profit from heterogeneity.

FOA outperforms our baseline for both data transfers and makespan criteria, in addition to the system utilization by up to two orders of magnitudes.

FOA minimizes cold start delays and speed up functions' execution time.


Said Jai-Andaloussi

Mathieu Lamard

Guy Cazuguel

Hamid Tairi

Mohamed Meknassi

B€atrice Cochener

Christian Roux

Content based Medical Image Retrieval: use of Generalized Gaussian Density to model BEMD's IMF

Keywords: Content-Based Image Retrieval, BEMD, Generalized Gaussian density, Kullback-Leibler distance

In this paper, we address the problem of medical diagnosis aid through content based image retrieval methods. We propose to characterize images without extracting local features, by using global information extracted from the image Bidimensional Empirical Mode Decomposition (BEMD). This method decompose image into a set of functions named Intrinsic Mode Functions (IMF) and a residu. The generalized Gaussian density function (GGD) is used to represent the coefficients derived from each IMF, and the Kullback-Leibler Distance (KLD) compute the similarity between GGDs. Retrieval efficiency is given for different databases including a diabetic retinopathy, and a face database. Results are promising: the retrieval efficiency is higher than 85% for some cases.

I. INTRODUCTION

Nowadays, medical systems produce a great amount of data images. Fast access to such huge databasse requires efficient indexing algorithms. CBIR system (Content-Based Image Retrieval) is one of the possible solutions to effectively manage image databases [START_REF] Nastar | Indexation d'images par le contenu: un etat de l'art[END_REF], [START_REF] Smeulders | Contentbased image retrieval at the end of the early years[END_REF]. The purpose is to retrieve desired images from databases using only the numerical content of images. Typical CBIR systems can be decomposed in two steps: at first, extraction of features from each medical image in the image database; then, the feature vector of a query image is computed and compared to the images feature vectors of the database. For definition and extraction of visual features, many methods have been proposed, includind image segmentation and image characterization using wavelet transform and gabor filter bank [START_REF] Smeulders | Contentbased image retrieval at the end of the early years[END_REF][START_REF] Lamard | Use of jpeg-2000 wavelet compression scheme for content-based ophtalmologic retinal retrieval[END_REF][START_REF] Lamard | Content Based Image Retrieval based on Wavelet Transform coefficients distribution[END_REF][START_REF] Jai-Andaloussi | Recherche d'images m€dicales par leur contenu num€rique : utilisation de signatures construites ‡ partir de la bemd[END_REF][START_REF] Manjunath | A texture descriptor for browsing and similarity retrieval[END_REF],

Recently, a novel multiresolution decomposition method, the Empirical Mode Decomposition (EMD), was introduced by Huang and al [START_REF] Huang | The empirical mode decomposition and the Hilbert spectrum for non linear and non-stationary time series analysis[END_REF]. The EMD is an adaptive decomposition which decompose any signal into a redundant set of signals denoted IMF and a residue. The original signal may be reconstruct by adding all the IMFs together and the residue, without information loss or distortion. EMD does not use any pre-determined filter or basis functions, which is quite different from Fourier analysis and wavelet analysis. In 2003, Nunes and al. [START_REF] Nunes | Image analysis by bidimensional empirical mode decomposition[END_REF] extend the 1D-EMD signal analysis to bidimensional signals and specifically to image processing (Bidimensional Empirical Mode Decomposition : BEMD). We propose in this work a new medical retrieval method which takes advantage of image BEMD. Wouwer and al. [START_REF] Wouwer | Statistical texture characterization from discrete wavelet representations[END_REF] used generalized Gaussian density functions (GGD functions) to represent texture images in the wavelet domain. In this paper we propose a new algorithm, based on Wouwer work, using BEMD decomposition instead of wavelet transform.

The setup of the paper is as follows. Section II-A describes the database we used for evaluation. Section II-B describes the BEMD method. Section II-C explains how to use GGD functions to represent the coefficients derived from BEMD. The retrieval method and Kullback-Leibler distance are described in section II-D and results are given in section III. We end with a discussion and conclusion in section IV.

II. MATERIAL AND METHODS

A. Databases

Two databases are used to test our method. 1) Diabetic retinopathy database: the diabetic retinopathy database, developed specifically in our team, contains retinal images of diabetic patients, with associated contextual anonymized information on the pathology. The database is made up of 63 patient files, containing 1045 photographs alltogether, and is divided in 6 levels of disease severity (6 classes). Images have a definition of 1280 pixels/line for 1008 lines/image. The patients were seen in consultation in Brest university hospital (France), within the screening or the follow-up of diabetic patient. The images were acquired wc2009paper-cor_GC_V2.doc by experts using a Topcon Retinal Digital Camera (TRC-50IA) connected to a computer. An example of image series is given in Fig 1. 2) FaceDataBase: This database [START_REF] Samaria | Parameterisation of a stochastic model for human face identification[END_REF] is used as a benchmark database. There are ten different images of each of 40 distinct subjects. For some subjects, the images were taken at different times, varying the lighting, facial expressions (open / closed eyes, smiling / not smiling) and facial details (glasses / no glasses). All the images were taken against a dark homogeneous background with the subjects in an upright, frontal position (with tolerance for some side movement). Images have a resolution of 92x112 pixels; each pixel is coded on a byte.

B. BEMD

The EMD method is an adaptive decomposition which allows to decompose any signal into a redundant set of signals denoted IMF and a residue. These IMFs are obtained by means of an algorithm called sifting process. Given a signal s(t), the sifting process of EMD can be summarized as follows. (c) Compute upper envelope and lower envelope funtions x i-1 and y i-1 by interpolating, respectively, local minima and local maxima of h i-1 ; (d) Compute m i-1 = (x i-1 +y i-1 )/2 (mean envelope), (e) Update h i =h i-1 -m i-1 and i=i+1; (f) Calculate stopping criterion (standard deviation SD ji ) (g) Repeat steps (b) to (f) until SD ji ≤ SDMAX and put then s j =h i (jth IMF) 4. Update residual r j =r j-1 -s j ; 5. Repeat steps 2-4 with j=j+1 until the number of extrema in r j is less than 2.

After IMFs are extracted through the sifting process, the original signal s(t) can be represented like this:

s (t )  Im f j (t) j  1 n   r (t ) (1 )
The Standard Deviation (SD) is the criteria to stop sifting process, computed from two consecutive sifting.

  2 K ( 1) 2 ij 2 1 ( 1) (2)
| ( ) ( ) | SD = ( )

j i ji k j i h k h k h k             
Fig. 3 BEMD applied to a part of a retina image: example Following Nunes and al. [START_REF] Nunes | Image analysis by bidimensional empirical mode decomposition[END_REF], the bidimensional sifting process is defined as follows :

wc2009paper-cor_GC_V2.doc  Identify the extrema (maxima and minima) of the image I.  Generate the 2D 'envelope' by connecting maxima points (respectively, minima points) with 2D interploation methods.  Averaging the two envelopes to compute the local mean m 1 .  Since IMF should have zero local mean, subtract out the mean from the image: I -m 1 = h 1 .  repeat as h 1 is an IMF.

In this paper we use the fast and adaptive BEMD presented in [START_REF] Bhuiyan | A novel approach of fast and adaptive bidimensional empirical mode decomposition[END_REF]. We give in Fig 3 an example of the BEMD for a retinal image.

C. Numerical image characterization : signatures

In this paper we suggest to characterize globally images by generating a numerical signature of image, based on IMFs contents. Wouwer and al. [START_REF] Wouwer | Statistical texture characterization from discrete wavelet representations[END_REF] show that, for textured images, the distribution of coefficients in the subbands of the wavelet transform may be modeled by a generalized gaussian law. Empirically, we noticed that the distribution of coefficients derived from IMFs seems also to follow a generalized gaussian law as illustrated below. The gaussian generalized law is derived from the normal law and parameterized by:  α: a scale factor, it corresponds to the standard deviation of the classical Gaussian law.  β: a shape parameter.

So the law density is defined as.

(3) 1 ; , 2 ( )

x x P e                           Where (.)  is the gamma function,   0 , t z t z e t dt       z>0
We propose to characterize images by using a maximum likelihood estimator

( , )

  of the distribution law for coef- ficients of each IMF of the BEMD decomposition [START_REF] Lamard | Content Based Image Retrieval based on Wavelet Transform coefficients distribution[END_REF]. These estimators are defined like this: given x= (x 1 , ..., x L ) the BEMD coefficients for one IMF. As x having independent component, Varanasi and Aazhang [START_REF] Varanasi | Parametric generalized gaussian density estimation[END_REF] demonstrated that ( , )   is the unique solution of equation ( 3).

1 1 1 ˆˆ| | 1 ˆ(4) i i L x L                          1 1 1 log | | | | log | | 0 | | i i i i i i i L L L x x x L x                     where (.)  is the digamma function ( ) ( ) ( ) z z z      .
 value should be find first by a Newton-Raphson algorithm. If the Newton-Raphson iterative algorithm is well initialized, it converges with few iterations. We defined the image vector signature by the couple ( , )   derived from each IMF.

A. Distance

To compute the similarity distance between to IMFs (Generalized Gaussian) and, according to [START_REF] Do | Wavelet-Based Texture Retrieval Using Generalized Gaussian Density and Kullback-Leibler Distance[END_REF] Kullback-Leibler distance is used (see equation ( 5)).

            ; ; || ; ; log (5) ; q q i q i p X KL p X p X p X dx p X       
In the case of generalized gaussian distributions, we inject equation (3) in equation ( 5), to obtain the following distance (equation ( 6)):

      2 2 1 2 2 1 1 1 1 2 2 2 1 2 1 1 1 1 1 1 ; , || ; , log - 1 1 (6) p X p X KL                                                                     wc2009paper-cor_GC_V2.doc
The distance between two images 1 I and 2 I is the sum of the balanced distance between IMFs.

 

1 2 1 1 2 2 1 ( , ) = ( , , ), ( , , ) (7)
K K K K k K k I I KLD p X p X D       
where k  are the adjustment weights.

III. RESULT

The method is tested on the two databases (see II-A), and is compared with previous methods detailed in [START_REF] Lamard | Content Based Image Retrieval based on Wavelet Transform coefficients distribution[END_REF][START_REF] Jai-Andaloussi | Recherche d'images m€dicales par leur contenu num€rique : utilisation de signatures construites ‡ partir de la bemd[END_REF].

The evaluation criteria is the mean precision at 5, which is the ratio between the number of pertinent images recalled and the total images recalled (here 5).

1) Each image in the database is used as a query image.

2) The algorithm find the five first images of the database closest to the query image. 3) Precision is computed for this query. 4) Finally, we compute the mean precision. From Table 1 we can see that a method based on adapted wavelets [START_REF] Quellec | Optimal wavelet transform for the detection of microaneurysms in retina photographs[END_REF] achieved the highest means precision 95.5% for face database with Adapted wavelets-GG, and 52.40% for retinas database with BEMD-Gabor method.

Extracting all IMFs of retinas database takes 1 day, and few minutes for face database. Then query is very fast. For this experiment we used C++ language on a AMD Athlon 64 X2 dual Core processor working on 2 GHz with 2 Gb DRAM.

IV. CONCLUSION

In this paper, we proposed a new method to characterize the numerical content of medical images, where BEMD coefficients in each IMF are independently modeled by a generalized Gaussian density law (GGD). To compute the measure of similarity between GGDs, we used the Kullback-Leibler Distance (KLD). BEMD-GGD functions pro-posed in this paper achieved encouraging experimental results.

For that purpose, our future work is to try to enhance retrieval results, by, first, optimizing adjustment weights (genetic algorithms). And second, by fusing of semantic (clinical data) and image numerical content.

Fig. 1

 1 Fig. 1 Photograph series of a patient eye

Fig. 2

 2 Fig. 2 Ten images sequence of the same person's face

1 .

 1 Initialise: r 0 = s (the residual) and j=1 (index number of IMF), 2. Extract the jth IMF: 3. (a) Initialise h 0 =r j-1 ; i=1; (b) Extract local minima/maxima of h i-1 ;

Fig. 4 BEMD

 4 Fig. 4 BEMD IMFs coefficients histogram example for the image decomposed in Fig 3.

Table 1

 1 Mean precision at 5.

Database


FOA: Function Orchestration Algorithm

Assumptions:

1) Functions and environments are independent and known in advance;

2) Their cost and processing time on each machine are known;

3) The dependency between functions and environments is known. Evaluation of scheduling policies FOA, K8S ImageLocality (baseline):

*The

In

  Minimum Cost Integral Matching phase uses the Dual-Approx. Algorithm of Shmoys and Tardos [D. B. Shmoys and E. Tardos, "An approximation algorithm for the generalized assignment problem," Math. Program., vol. 62, no. 1-3, p.461-474, Feb. 1993]. Anderson Andrei DA SILVA, Y. Georgiou, M. Mercier, G. Mounié, D. Trystram Towards an Energy-Aware Multi-objective Scheduling Policy for Server-based Edge-Cloud Continuum Experimental Protocol Adaptation of the benchmark FunctionBench ¹, Deployment of OpenWhisk ² on GRID5000 ³, Measurement and calibration of results.

Table 1

 1 Design of Experiments. Total of 1620 experiments.

	Parameters	Values
	Workload Size	200, 600, 1000
	Platform Size	100, 300, 500
	Heterogeneity Level	3, 5, 7
	Scheduling Policies	FOA, K8S ImageLocality
	Random Seeds	30

a simulated environment, On top of Batsim/ Simgrid [H.Casanova et.al, 2014]. ¹ https://github.com/kmu-bigdata/serverless-faas-workbench , ² https://openwhisk.apache.org/, ³ https://www.grid5000.fr . Anderson Andrei DA SILVA, Y. Georgiou, M. Mercier, G. Mounié, D. Trystram Towards an Energy-Aware Multi-objective Scheduling Policy for Server-based Edge-Cloud Continuum 7 / 17

Table 1

 1 Design of Experiments. Total of 1620 experiments.

	Function	Input Values	Unit
	Chameleon	2.10 3 , 3.10 3	Matrix size
	Float operation	10.10 7 , 20.10 7 , 30.10 7	Operations
	Image processing	60, 40	Image size in MB
	Linpack	5.10 3 , 6.10 3	Matrix size
	Matrix Multiplication	3.10 3 , 4.10 3	Matrix size
	Model Training	50, 100	Dataset size
	Pyaes	3.10 3 , 4.10 3 , 5.10 3	Length of message
	Video Processing	30, 50, 100	Video size in MB

Table 2 :

 2 Functions adapted from FunctionBench.Experimental results: Linear program trade-off

				Workload Size = 200
				Platform Size = 500
	Amount of Downloaded Data (GB)	0 50 100 150 200
		0	50	100		150
				Makespan (Minutes)
			LP Binary Search Iteration	1 5	2 6	3 7	4 8

Anderson Andrei DA SILVA, Y. Georgiou, M. Mercier, G. Mounié, D. Trystram Towards an Energy-Aware Multi-objective Scheduling Policy for Server-based Edge-Cloud Continuum 7 / 17

Anderson Andrei DA SILVA, Y. Georgiou, M. Mercier, G. Mounié, D. Trystram Towards an Energy-Aware Multi-objective Scheduling Policy for Server-based Edge-Cloud Continuum

Anderson Andrei DA SILVA, Y. Georgiou, M. Mercier, G. Mounié, D. Trystram


Nathalie Conil

Clara Maghami

Philippe Gombert

Marwan Al Heib

Impact of climate change on the collapse of shallow minesfeedback from France

Keywords: shallow abandoned mines, aging, collapse, climate change, water-rock interaction

For many years, Ineris has been conducting research on the impact of climate change on the stability of abandoned mines. In this context, work has been initiated to reference cases of shallow mine collapses. So far, 480 cases have been identified and described. Preliminary analysis of the information gathered shows that 50% of the cases correspond relate to chalk mines, 32% to limestone mines, and 16% to gypsum mines. Two case studies presented in the paper were also analyzed in more detail. Complexity of the water-rock interaction and the importance of studying more precisely the various parameters impacted and their relationships are highlighted. Therefore, a chalk mine located in Seine-et-Marne (France) was instrumented to monitor the evolution of the structure over time and analyze the different causes of degradation. The objectives are to better understand the behavior of these structures to be able to detect precursor signs to these collapses.

INTRODUCTION

The collapse of underground shallow cavities may represent an important geohazard for people and infrastructures. The number of cavities is estimated at more than 500,000 in the French subsoil, many of which are abandoned shallow mines. Some are excavated in rocks that are particularly sensitive to water (gypsum, chalk, limestone). With ongoing climate change, we expect an increased frequency of exceptional hydroclimatic events (intense droughts, heavy rains, or floods) that can create high amplitudes in groundwater tables or stream levels or cause important water infiltrations. All these phenomena are likely to increase the risk of instability of water-sensitive mines. The challenges related to this risk are generally high, particularly in human and socio-economic terms. [START_REF] Josien | Diagnostic et caractérisation des aléas[END_REF] discusses the possible role of water as an initiating mechanism (loading of the overlying water tables in roof ruptures, modification of the properties of the rock floor rupture) or as an aggravating factor (variations in the rock water content, in the water table or hygrometry, circulation or condensation of water in the case of marly clay interlayers). [START_REF] Vincent | Caractérisation de l'aléa lié à la présence de carrières souterraines abandonnées en périphérie immédiate de la ville de Saint-Emilion (Gironde)[END_REF] cite several collapses that occurred in 1897 in St-Emilion (Gironde), after an extremely rainy winter. Léotot (2016) highlights to the role of the rise of water table or roof infiltration in several collapses near Châtellerault (Vienne). [START_REF] Noury | Les mouvements de terrains liés aux marnières en Seine-Maritime et dans l'Eure -Etablissement de chroniques et réflexion sur l'influence des intempéries[END_REF] analyze the impact of the unusually rainy periods of 1994-1995 and 2000-2001 on the breaking of "marnières1 " pits in Normandy. The case of Château-Landon, southeast of Paris, illustrates the complexity of the process of interaction between the meteorological factor and the predisposition to mine instability. Over only 1 km, 3 of the 4 chalk mines collapsed between 1878 and 1910 in connection with heavy rains and floods [START_REF] Kreziak | Analyse et interrogations liées à l'effondrement de la carrière souterraine de craie de Lorroy en 1910[END_REF].

For several years, Ineris has conducted research on the stability of abandoned mines related to climate change. A catalog of water-sensitive mine collapses was compiled to analyze the link between climate and the degradation of underground structures. A study of the hydroclimatic conditions was conducted for two historic French collapses (Château-Landon in 1910, Clamart in 1961). Finally, a mine was instrumented by Ineris in 2019 in Château-Landon, in collaboration with Cerema (Centre for Studies on Risks, the Environment, Mobility and, Urban Planning), to study its evolution and identify potential precursor signs of instability [START_REF] Conil | An underground research laboratory at Château-Landon (France) to study the impact of climate change on the stability of abandoned mines[END_REF]).

INVENTORY OF COLLAPSES IN FRANCE

Within the framework of this study, a catalog of large-scale collapses (>10 m in diameter) of mines was compiled. These collapses have been selected from the Internet (newspaper articles, reports, etc.) as well as from scientific articles. The catalog includes data on:

• mine environment: department, municipality, locality, geographical coordinates, geological and hydrogeological context; • mine features: surface area, mining depth, the average height of galleries, mining mode, mine closure date, extraction rate, and material mined; • collapses: geographical coordinates, date of occurrence, the area concerned, depth, description, bibliographical reference, distance to the nearest river, geomorphological location (valley, slope, plateau, etc.), possibly the climatic conditions in the period preceding the collapse, known damage and casualties.

At this stage of the study, the catalog includes 480 collapses, 50% of which correspond to chalk mines, 32% limestone, and 16% gypsum. Preliminary analyses show an average extraction rate of more than 50%, which means the pillars are very stressed (Figure 1).

IMPACT OF CLIMATIC CONDITIONS -PRELIMINARY STUDY

Preliminary analysis of the data shows that several collapses were preceded by heavy rain events some days or weeks earlier. A correlation was investigated between the occurrence of the 139 collapses dated with daily precision and the 447 main rainy events recorded by Météo France (the French national meteorological service) since 1766. Only 3 collapses could be unambiguously linked to the occurrence of one of these extreme events:

• The collapse of the chalk mine of Château-Landon, which occurred during the historic flood of the Seine and its tributaries which lasted from January 18 to February 26, 1910; • The opening of a sinkhole on September 1 st , 2010 on the surface of a chalk mine in Châlons-en-Champagne (Marne), in connection with heavy rainfalls that occurred two weeks earlier with local intensities of more than 100 mm of water in 48 hours; • The collapse of a limestone mine in Gidy (Loiret) in 2016 during a heavy rainfall period.

Based on these, the probability that an extreme climatic event could be the direct cause of a mine collapse would be in the order of percent. Although the precise date of most collapses in the list is unknown, the analysis shows that it is difficult to invoke the role of extreme precipitation in collapses: if water plays a role, it must be analyzed over a longer period.

A complementary approach was therefore undertaken. Among the collapses dated to the nearest day, this approach consisted of identifying observations related to degraded weather conditions, such as heavy but not exceptional rains. Out of 86 observations, 13 referred to such. This means that 15% of the collapses occurred in abnormally rainy climatic conditions. Next, the possible impact of long periods of drought will also be examined. To verify the correlation between rainfall events and the collapse of underground cavities, 2 case studies were selected: Château-Landon in Seine et Marne and Clamart in Hauts de Seine. Their location is shown in Figure 2.

RETRO-ANALYSES OF TWO COLLAPSES

CLAMART (1961)

On June 1st, 1961, a chalk mine suddenly collapsed in Clamart (Hauts-de-Seine) and led to the destruction of an urban district, killing 21 people and injuring more than fifty. The mine, which was mined until 1880, is located on the edge of a chalk hillside topped with tertiary land and overlooking the Seine valley [START_REF] Heib | Analysis of the historical collapse of an abandoned underground chalk mine in 1961 in Clamart[END_REF]. It comprises an upper level of around 37 m NGF, mined to the south and north according to a very regular pattern and with an extraction rate of 55% to 68%, and a lower level of around 29 m NGF, mined in the southern part with very irregular pillars and an extraction rate of 36% to 51%. There are three aquifers here: the alluvial aquifer of the Seine with a water table around 30-33 m asl, the chalk aquifer, which is in hydraulic continuity about 5 m above, and the layer of Lutetian limestone, separated from the previous ones by about fifteen meters of impermeable formations.

Having been studied extensively, the causes of this mine collapse have never been established with certainty, but experience-based feedback on the possible role of water has been considered. For several years, the lower level of the mine had been flooded by the chalk water table, but its level did not vary before the collapse, just as with the level of the Seine, which was low. However, precipitation was contrasted during the 8 years preceding the collapse with the driest year (400 mm in 1953) and the wettest year (812 mm in 1958) for the entire period 1941-1960. In the month preceding the collapse, significant precipitation concentrated in a small number of days was recorded: there was more precipitation during the week preceding the collapse than in a normal month, in particular with 48 mm on May 25. Although no exceptional hydroclimatic event occurred, this elevated rainfall a week before the collapse could have played a role, as well as the two water system leaks reported to the right of the mine during the days leading up to it (Figure 3).

CHATEAU LANDON (1910)

The collapse of the Beaulieu chalk mine in Château-Landon in 1910 followed 3 other collapses of the same type, which occurred in 1878 and 1897 over a section approximately 1 km long. This abnormal succession of disorders shows a particular sensitivity of this sector where the chalk is known to be very sensitive to moisture conditions [START_REF] Lafrance | Study of the effects of water on the phenomena of rupture and deformation affecting underground chalk quarries[END_REF]. These collapses probably result in part from the hydrogeological context of the mines that were excavated at the base of the slope, only a few meters above the water table and the alluvial plain. They occurred during a succession of comparable hydroclimatic events (Figure 4): a very rainy month (94 mm in 1876, 48 mm in 1897, 122 mm in 1910) which saturated the ground and recharged the aquifers, then heavy flooding of the Loing (river passing nearby the mines) the day before each collapse with respective maximum heights of 1.4 m, 3.3 m, and 3.9 m. The disaster scenario proposed by Gombert & Cherkaoui ( 2011) is as follows: (i) the Loing flood creates a hydraulic dam which (ii) prevents the chalk water table from flowing horizontally and (iii) forces its level to rise, until (iv) it overflows at the lower parts of the mine. The soaking of the base of the pillars completely saturated the chalk (v), reducing its compressive strength and causing the collapse of this area (vi). The rest of the slope, more stable but undermined, then lost its eastern abutment and suffered a landslide (vii) which buried a hamlet.

Conclusions of the case study

These results show that collapses can be controlled by an accumulation of parameters that are not always well-identified. Thus, the case of Clamart shows that a period of drought followed by heavy rainfall could have accelerated the process of degradation of the structure, without being the main cause of the disaster, but a likely triggering factor [START_REF] Heib | Analysis of the historical collapse of an abandoned underground chalk mine in 1961 in Clamart[END_REF]. The cases of Château-Landon and Clamart collapses show that the geometry of the exploitation is a predisposing factor, as well as the initial and modified mechanical properties of the massif and the overburden. [START_REF] Nguyen | Influence des interactions eau-roche sur le comportement à long terme de cavités souterraines dans la craie[END_REF] showed that variations in atmospheric relative humidity in the chalk mine of Estreux (59) could modify the saturation level of the massif. As for the heavy rains and associated flooding, they are the cause of the collapses of Château-Landon.

CHATEAU-LANDON OBSERVATORY

To better understand mines degradation, monitoring the in-situ behavior of an abandoned mine seemed necessary to supplement the knowledge of aging kinetics. The selected site is the Royer mine, located in Château-Landon [START_REF] Conil | An underground research laboratory at Château-Landon (France) to study the impact of climate change on the stability of abandoned mines[END_REF], close to the historical catastrophic collapses from 1878 to 1910. The chosen site also presents several similarities with the Beaulieu mine, in terms of geomorphology, exploited chalk (it is particularly watersensitive), and exploitation method.

The mine is heavily fractured. This fracturing affects the pillars as well as the roof of the galleries, with the backfill hiding the fracturing at their base. More than three-quarters of fractures are without displacement (diaclases), the majority being closed. Split-level fractures are normal, radial, or stepped flaws, showing openings and level differences of a few mm to cm. The preliminary risk assessment analysis showed that the mine is susceptible to hydroclimatic phenomena.

Two types of parallel monitoring were set up at the end of 2019 to correlate water data (variations in water table, water content of the chalk, and hygrometry) and acquired geotechnical data (deformation and failure of a pillar, a roof, and a fault). More than 50 sensors are installed in 3 different areas called A, B, and C as well as outside the mine (Figure 5a): A is the small pillars area, B is the fault area, and C is the control area. All the data are shared through a dedicated webmonitoring page on the e.cenaris (https://cenaris.ineris.fr) web portal. Fluctuations in the level of the chalk water table, which correspond to the high water / low water cycles, reach ±2.77 m upstream and ±0.78 m downstream where they are buffered by those of the Loing river (±0.87 m) which forms the base level of the aquifer (Figure 5a). The figure also includes the distance variation measurements from the vault of the gallery to the embankment (zone C) and at the level of the fault plane (zone B). A correlation is observed between the piezometric cycles and the level of the embankment as well as the displacements of the fault plane (Figure 5b).

The impact of climatic events on potentially unstable underground cavities has been widely studied.

Nevertheless, important scientific gaps remain, concerning the origins of the collapses of shallow abandoned cavities. To better evaluate this impact, Ineris carried out a dedicated research program that includes referencing large collapse events. To date, 480 cases have been identified. Preliminary analysis shows that collapses concern mainly cavities with a high extraction ratio (> 50%) and particularly the chalk mines. Additionally, even if water has a significant role in the collapse process, exceptional climate event is rarely a triggering factor of the event. It seems that a long period of rainfall has more impact. The analysis of different case studies also shows that the impact of water is not always well understood and is often coupled with many other parameters which are important to better estimate the probability of such disaster. The research program also includes the Chateau Landon observatory which is located near the collapses of old mines that occurred between 1878 and 1910. The measurements show a good correlation between cavity deformation and the water table variation and highlight the necessity to improve our knowledge of the aging of these structures to understand the different phenomena and their coupling which can lead to such events.

Figure 1 .

 1 Figure 1. (a) Distribution of mined materials for 473 mines (b) Extraction ratio for 145 mines.

Figure 2 .

 2 Figure 2. Ineris instrumented sites (in blue) -collapsed mines selected as case studies (in red).

Figure 3 .

 3 Figure 3. (a) Monthly rainfall from 1960 to June 1961 and (b) Clamart collapse on June 1st, 1961.

Figure 4

 4 Figure 4. a) Rainfall and height of the Loing before the collapse of Château Landon in 1910, b) Location of the underground mines.

Figure 5 .

 5 Figure 5. (a) Instrumentation of the Royer mine and (b) comparative evolution of the mean movements of the backfill and the fault plane with the daily heights of the water table and the river.

Chalk mines generally comprise a vertical access shaft and one or more horizontal chamber(s).

ACKNOWLEDGMENTS

The authors thank the Ministry of Ecological Transition for its financial support in this study. They also thank the department of Seine et Marne, the owner of the "Royer" mine, and the local association for the protection of bats, for their support in the installation and maintenance of the Chateau Landon Observatory project. Data acquisition and processing performed in this observatory are based on the Cenaris infrastructure (https://cenaris.ineris.fr).