Alison Pereira

Sébastien Nomade

Christophe Falguères

Jean-Jacques Bahain

Olivier Tombret

Tristan Garcia

Pierre Voinchet

Grazia-Maria Bulgarelli

Anna-Paola Anzidei

ESR/U-series data for the La Polledrara di Cecanibbio archaeological

est destinée au dépôt

Introduction

La Polledrara di Cecanibbio is one of the numerous Middle Pleistocene sites of the Roman area, Italy. It was discovered in 1984 through a program of territorial surveys led by the "Soprintendenza per i Beni Archeologici di Roma". After thirty years of excavation campaigns, La Polledrara di Cecanibbio is currently considered as one of the richest deposit of the Lazio province but also as one of the landmark sites from the Italian Middle-Pleistocene period [START_REF] Anzidei | Nouvelles données sur le gisement Pléistocène moyen de La Polledrara di Cecanibbio (Latium, Italie)[END_REF][START_REF] Anzidei | Ongoing research at the late Middle Pleistocene site of La Polledrara di Cecanibbio (central Italy), with emphasis on human elephant relationships[END_REF][START_REF] Santucci | Palaeoloxodon exploitation at the Middle Pleistocene site of La Polledrara di Cecanibbio (Rome, Italy)[END_REF]. > 20,000 palaeontological fossils and at least 1100 lithic tools and bones artefacts were identified. It is worth mentioning that La Polledrara di Cecanibbio is characterized by the absence of bifacial tools [START_REF] Anzidei | Ongoing research at the late Middle Pleistocene site of La Polledrara di Cecanibbio (central Italy), with emphasis on human elephant relationships[END_REF]. Furthermore, several Palaeoloxodon antiquus carcasses trapped in muddy sediments demonstrate hominids scavenging traces highlighting the opportunistic behaviours of the Pre-Neanderthal populations. These impressive numbers of well-preserved fossils and tools as well as the testimony of opportunistic behaviours with respect to elephants' skeletons underline the exceptional nature of this deposit within the corpus of Italian's Lower Palaeolithic sites [START_REF] Anzidei | Ongoing research at the late Middle Pleistocene site of La Polledrara di Cecanibbio (central Italy), with emphasis on human elephant relationships[END_REF][START_REF] Santucci | Palaeoloxodon exploitation at the Middle Pleistocene site of La Polledrara di Cecanibbio (Rome, Italy)[END_REF]. Since 2000, a building covering 900 m 2 of the site palaeo-surface is accessible to the public and allows the site protection.

Current geological and palaeontological constraints allowed the attribution of La Polledrara di Cecanibbio to the Aurelian formation. This site was estimated by biochronology between 340 and 320 ka, corresponding to marine isotopic stage (MIS) 9 [START_REF] Anzidei | Ongoing research at the late Middle Pleistocene site of La Polledrara di Cecanibbio (central Italy), with emphasis on human elephant relationships[END_REF]. However, the chronology of La Polledrara must be refined by geochronological data derived from absolute dating technics as without accurate chronological data the comparison of La Polledrara di Cecanibbio with the numerous nearby sites contemporaneous with this time period remains still hazardous (e.g. [START_REF] Villa | The Acheulian and early Middle Paleolithic in Central Italy: stability and innovation[END_REF]. In 2012, in the frame of an Italian/French collaboration, we started a large program of geochronology that aims at creating a more robust chronological framework for the corpus of Italian's Lower Palaeolithic sites. We will present in this contribution the detail results obtained for La Polledrara di Cecanibbio using the 40 Ar/ 39 Ar on single-grains and the ESR/U-series methods on dental tissues; replacing this site in a precise palaeo-climatological context and in the frame of the Roman area's Lower Palaeolithic sites corpus.

Geological setting

Geological context of the Lazio province

La Polledrara di Cecanibbio is located in the Lazio, close to Rome. This region, hosting the delta of the Tiber River since the beginning of the Middle Pleistocene (e.g. [START_REF] Milli | Depositional setting and high-frequency sequence-stratigraphy of the Middle-Upper Pleistocene to Holocene deposits of the Roman Basin[END_REF][START_REF] Marra | The subsurface geology of Rome: sedimentary processes, sea-level changes and astronomical forcing[END_REF], Marra et al., 2016), is particularly rich in Middle Pleistocene archaeological sites such as Torre in Pietra, Malagrotta, Castel di Guido or Casal de'Pazzi (e.g. [START_REF] Manzi | The Casal de'Pazzi archaic parietal : comparative analysis of new fossil evidence from the late Middle Pleistocene of Rome[END_REF][START_REF] Anzidei | Two Middle Pleistocene sites near Rome (Italy): La Polledrara di Cecanibbio and Rebibbia-Casal de Pazzi[END_REF][START_REF] Boschian | Ambiguities in human and elephant interactions? Stories of bones, sand and water from Castel di Guido (Italy)[END_REF], Villa et al., 2016, Fig. 1). In fact, this particular geological context allows the deposition of lacustrine fluviosedimentary successions, in response to the strictly interaction among the glacio-eustatic variations, the tectonic uplift, and the volcanism along the Latium Tyrrhenian margin, so allowing a good correlation with the marine isotopic stages [START_REF] Milli | Depositional setting and high-frequency sequence-stratigraphy of the Middle-Upper Pleistocene to Holocene deposits of the Roman Basin[END_REF]Palombo, 2005;[START_REF] Marra | Independent 40 Ar/ 39 Ar and 14 C age constraints on the last five glacial terminations from the aggradational successions of the Tiber River, Rome (Italy)[END_REF], Marra et al., 2014). The continued uplift of this region since 800 ka, allows a good exposure of sedimentary successions making this region one of the richest of the Italian peninsula harboring mammalian fauna as well as testimonies of human activities (Marra et al., 2014). [START_REF] Villa | The Acheulian and early Middle Paleolithic in Central Italy: stability and innovation[END_REF][START_REF] Manzi | The Casal de'Pazzi archaic parietal : comparative analysis of new fossil evidence from the late Middle Pleistocene of Rome[END_REF][START_REF] Anzidei | Two Middle Pleistocene sites near Rome (Italy): La Polledrara di Cecanibbio and Rebibbia-Casal de Pazzi[END_REF][START_REF] Barbattini | Nuovo giacimento del Paleolitico inferiore in Agro Castel di Guido (Roma)[END_REF][START_REF] Saccà | Taphonomy of Palaeloxodon antiquus at Castel di Guido (Rome, Italy): proboscidean carcass exploitation in the Lower Palaeolithic[END_REF][START_REF] Ceruleo | The archaic Acheulean lithic industry of the Cretone basin (Latium, central Italy)[END_REF] and with the active volcanic complexes of the Middle Pleistocene [START_REF] Karner | The history of the Monti Sabatini and Alban Hills volcanoes: groundwork for assessing volcanic-tectonic hazards for Rome[END_REF][START_REF] Sottili | Geochronology of the most recent activity in the Sabatini Volcanic District, Roman Province, central Italy[END_REF][START_REF] Marra | The Alban Hills and Monti Sabatini volcanic products used in ancient Roman masonry (Italy): an integrated stratigraphic, archaeological, environmental and geochemical approach[END_REF].

These specific archaeological deposits are, according to [START_REF] Milli | The high-resolution sequence stratigraphy and the mammal fossil record: a test in the Middle-Upper Pleistocene deposits of the Roman basin[END_REF], related to the informal sequence stratigraphic unit known in the literature as Ponte Galeria Sequence (PGS). Oriented northwest-southeast on 30 km along the Tyrrhenian Sea margin, this sequence was subdivided in twelve depositional sequences limited above and below by unconformity surfaces [START_REF] Milli | From river to shelf, anatomy of a high-frequency depositional sequence: the Late Pleistocene-Holocene Tiber Depositional Sequence[END_REF]. La Polledrara di Cecanibbio was attributed in the literature to the informal lithostratigraphic unit Aurelia formation, MIS 10/9 whose limits are equal to the PG6 sequence-stratigraphic unit, mainly composed of fluvial and fluviopalustrine deposits rich in volcanic material [START_REF] Milli | Depositional setting and high-frequency sequence-stratigraphy of the Middle-Upper Pleistocene to Holocene deposits of the Roman Basin[END_REF]Palombo, 2005).

The volcanic materials found at La Polledrara and in the major part of the Lazio's successions come from Roman volcanic districts very active between 450 and 300 ka [START_REF] Karner | The history of the Monti Sabatini and Alban Hills volcanoes: groundwork for assessing volcanic-tectonic hazards for Rome[END_REF][START_REF] Sottili | Geochronology of the most recent activity in the Sabatini Volcanic District, Roman Province, central Italy[END_REF][START_REF] Marra | The Alban Hills and Monti Sabatini volcanic products used in ancient Roman masonry (Italy): an integrated stratigraphic, archaeological, environmental and geochemical approach[END_REF]. La Polledrara di Cecanibbio like the neighbouring sites of Torre in Pietra and Castel di Guido is located in the marginal sector of the Monti Sabatini volcanic district and thus presents both reworked volcanic materials and primary fallouts rich in K-Feldspars allowing the use of the 40 Ar/ 39 Ar radio-isotopic method. Furthermore, [START_REF] Castorina | Geochemical and Sr/Nd isotopic characterization of Middle Pleistocene sediments from the paleontological site of La Polledrara di Cecanibbio (Sabatini Volcanic District, central Italy)[END_REF] suggested, on the basis on Sr isotopes analyses, that volcanic materials originated from Monti Sabatini have contributed to the sediments found at La Polledrara di Cecanibbio.

La Polledrara di Cecanibbio stratigraphy

The site of la Polledrara di Cecanibbio displays a 2 m thick stratigraphic succession composed of fluvial deposits rich in volcanic material (80 m a.s.l) (Fig. 2). The base of the stratigraphy is made of cross-laminated deposits characteristic of a small river channel (oriented W-NW to E-SE [START_REF] Anzidei | Nouvelles données sur le gisement Pléistocène moyen de La Polledrara di Cecanibbio (Latium, Italie)[END_REF]. A pit made outside the protected area demonstrated that this fluvio-lacustrine deposit overlaid a white volcanic level discovered 3 m below the fossiliferous area (POL 13-01, Fig. 2). This small river channel is currently filled by about 2 m of sediments rich in graded volcanic material, mainly composed by white altered graded blocks of pyroclastic material (Fig. 2). These blocks are very rich in sanidines, clinopyroxenes and apatites. Large size volcanic material blocks are at the base of the layer and the thinnest ones at the top of the level. The archaeological layer, characterized by its high composition in volcanic material, is described as fluvial-flood sediments by [START_REF] Anzidei | Ongoing research at the late Middle Pleistocene site of La Polledrara di Cecanibbio (central Italy), with emphasis on human elephant relationships[END_REF]. Fossils and artefacts were deposited following the river stream and piled when the flow decayed enough. In the higher part of the fossiliferous level, devoid of visible large volcanic material blocks, were discovered three Palaeoloxodon antiquus skeletons found in anatomical articulation [START_REF] Santucci | Palaeoloxodon exploitation at the Middle Pleistocene site of La Polledrara di Cecanibbio (Rome, Italy)[END_REF]. It proves that some animals were probably trapped later when this deposit became swampy [START_REF] Anzidei | Ongoing research at the late Middle Pleistocene site of La Polledrara di Cecanibbio (central Italy), with emphasis on human elephant relationships[END_REF] and was not totally consolidated [START_REF] Anzidei | Ongoing research at the late Middle Pleistocene site of La Polledrara di Cecanibbio (central Italy), with emphasis on human elephant relationships[END_REF]. The exceptional preservation state of the archaeological and palaeontological remains is explained by the preponderance in this deposit of volcanic material rich in fluorine [START_REF] Anzidei | Ongoing research at the late Middle Pleistocene site of La Polledrara di Cecanibbio (central Italy), with emphasis on human elephant relationships[END_REF][START_REF] Castorina | Geochemical and Sr/Nd isotopic characterization of Middle Pleistocene sediments from the paleontological site of La Polledrara di Cecanibbio (Sabatini Volcanic District, central Italy)[END_REF]. In fact, the high percentage of fluorine encompassing the bones allows the rapid exchanges of calcium to form fluoro-apatite [START_REF] Anzidei | Nouvelles données sur le gisement Pléistocène moyen de La Polledrara di Cecanibbio (Latium, Italie)[END_REF].

Palaeontological record

As mentioned above, > 20,000 vertebrate fossils were recovered at La Polledrara [START_REF] Anzidei | Nouvelles données sur le gisement Pléistocène moyen de La Polledrara di Cecanibbio (Latium, Italie)[END_REF][START_REF] Anzidei | Ongoing research at the late Middle Pleistocene site of La Polledrara di Cecanibbio (central Italy), with emphasis on human elephant relationships[END_REF]. The most represented taxa are Bos primigenius and Palaeoloxodon antiquus. Some other species like Stephanorhinus hemitoechus, Equus ferus, Sus scrofa, Cervus elaphus and Bubalus murrensis are also represented. Only few carnivores (Canis lupus and Vulpes vulpes) and primates (Macaca sylvanus) are mentioned. Concerning the micro-mammals species, arvicolids and murids were identified. Arvicolids species are Iberomys cf. I. breccensis, Pliomys cf. P. episcopalis and Arvicola sp. The only murid species found is Apodemus sylvaticus [START_REF] Anzidei | Nouvelles données sur le gisement Pléistocène moyen de La Polledrara di Cecanibbio (Latium, Italie)[END_REF][START_REF] Anzidei | Ongoing research at the late Middle Pleistocene site of La Polledrara di Cecanibbio (central Italy), with emphasis on human elephant relationships[END_REF]. The large palaeontological assemblage of La Polledrara di Cecanibbio is associated to the Torre in Pietra faunal unit related to the early "Aurelian mammals ages" [START_REF] Milli | The high-resolution sequence stratigraphy and the mammal fossil record: a test in the Middle-Upper Pleistocene deposits of the Roman basin[END_REF].

Archaeological record and evidence of human activities

Only one human tooth attributed to "Homo heidelbergensis" after the estimated age of the site [START_REF] Manzi | Early Middle Pleistocene environmental changes and human evolution in the Italian peninsula[END_REF] was found. This tooth is a deciduous second maxillary molar, belonging to a child aged between 5 and 10 years old [START_REF] Anzidei | Ongoing research at the late Middle Pleistocene site of La Polledrara di Cecanibbio (central Italy), with emphasis on human elephant relationships[END_REF]. > 1100 artefacts were unearthed, 500 pieces were collected mainly at the bottom of the archaeological layer and about 600 flint implements were found around the butchered elephant [START_REF] Anzidei | Ongoing research at the late Middle Pleistocene site of La Polledrara di Cecanibbio (central Italy), with emphasis on human elephant relationships[END_REF]. Concerning the tools discovered in both base and top of the fossiliferous deposit it is worth mentioning that they were made using flint and, more rarely, siliceous limestone little pebbles. The assemblage includes cores, pebble tools, flakes and retouched tools like denticulates, notches and scrapers. Like at Castel di Guido some tools are made of Palaeoloxodon antiquus bones [START_REF] Anzidei | Ongoing research at the late Middle Pleistocene site of La Polledrara di Cecanibbio (central Italy), with emphasis on human elephant relationships[END_REF]. One particularity of tools assemblages from La Polledrara di Cecanibbio is the lack of handaxes, present in other nearby sites of the Lazio (e.g. Torre in Pietra or Castel di Guido; Fig. 1, Anzidei et al., 2012, page. 181). Another characteristic of La Polledrara is the highlighting of the opportunistic nature of the Pre-Neanderthal populations. In fact, the most well-preserved elephant carcass is associated with a lithic industry that was produced in situ (cores, tools, flakes and working debris). Some of the flint implements associated present wear traces of use on animal tissues, document human activity related to the exploitation of the carcass by scavenging [START_REF] Anzidei | Ongoing research at the late Middle Pleistocene site of La Polledrara di Cecanibbio (central Italy), with emphasis on human elephant relationships[END_REF][START_REF] Santucci | Palaeoloxodon exploitation at the Middle Pleistocene site of La Polledrara di Cecanibbio (Rome, Italy)[END_REF]. Furthermore, the femurs show fracture morphology referable to human activity, indicating that these elements were exploited. The fracturing mode should be attributed to the shaping of the raw material and not just to simple fracturing for marrow exploitation. Finally, some bones of carcass are missing after the butchering episode because of natural factors, or by human activity [START_REF] Santucci | Palaeoloxodon exploitation at the Middle Pleistocene site of La Polledrara di Cecanibbio (Rome, Italy)[END_REF].

Palaeoenvironmental data

87 Sr/ 86 Sr and stable isotopes (δ 13 C and δ 18 O) analyses were made by [START_REF] Palombo | Coupling tooth microwear and stable isotope analyses for palaeodiet reconstruction: the case study of Late Middle Pleistocene Elephas (Palaeoloxodon) antiquus teeth from Central Italy (Rome area)[END_REF] on Palaeoloxodon antiquus dental enamel (twenty-three samples). These analyses confirmed the proximal origin of the volcanic products and suggested an intermediate diet for these elephants (herbs, leaves, bark) in agreement with a temperate and/or hot climate (i.e. interglacial conditions). New 87 Sr/ 86 Sr analyses performed on the matrix of the archaeological deposit by [START_REF] Castorina | Geochemical and Sr/Nd isotopic characterization of Middle Pleistocene sediments from the paleontological site of La Polledrara di Cecanibbio (Sabatini Volcanic District, central Italy)[END_REF] suggested different sources from the Monti Sabatini volcanic complex. However, the fact that they did not investigate the white volcanic blocks but only the matrix may explain the diversity of sources highlighted by this study for the archaeological level.

Material and methods

40 Ar/ 39 Ar on sanidines single grains

Three different layers were sampled for 40 Ar/ 39 Ar dating. The first one is the white volcanic layer located 1 m below the deepest archaeological remains (POL 13-01) (Fig. 2). The second sample was taken just under the archaeological layer within the reddish cross-laminated fluvial horizon very rich in volcanic material (POL 12-02). Finally, the last samples were taken within the archaeological layer itself [START_REF] Anzidei | Ongoing research at the late Middle Pleistocene site of La Polledrara di Cecanibbio (central Italy), with emphasis on human elephant relationships[END_REF]. For this layer (around 1.5 m thick, see Fig. 2) we decided to collect pieces of white volcanic material blocks in two different places (see Fig. 2). A large one (10 cm in diameter) was taken at the base of the archaeological layer (POL 12-03, Fig. 2) whereas smaller ones found 10 cm apart (POL 12-01) were taken closer to the top of the layer (i.e. 3 cm in diameter).

All the 40 Ar/ 39 Ar analyses were performed at the LSCE laboratory, Gif-sur-Yvette (France). Volcanic materials extracted from the archaeological deposit were separately prepared crushed and sieved. Clear and non-altered sanidine crystals ranging from 500 μm up to 1 mm in size were concentrated for each sample and handpicked under a binocular microscope. These sanidines were then leached for 5 min in a 7% HF acid solution in order to remove the possibly attached groundmass and then repeatedly rinsed with distilled water in an ultrasonic bath. At least 30 crystals were then chosen for each sample and separately loaded in aluminium disks. Samples POL 13-01 and POL 12-02 were irradiated for 40 min (IRR 77) in the β1 tube of the OSIRIS reactor (CEA Saclay, France) and samples POL 12-03 and POL-12-01 were irradiated for 1 h (IRR 66). After irradiation between 15 and 20 crystals for each sample were individually loaded in a copper sample holder. The sample holder was then put into a double vacuum Cleartran window. Each crystal was then fused using a Synrad CO 2 laser at 10 to 15% of nominal power (c.a. 25 W). The extracted gas was then purified for 10 min by two hot GP 110 and two GP 50 getters (ZrAl). Argon's isotopes ( 36 Ar, 37 Ar, 38 Ar, 39 Ar and 40 Ar) were analysed by mass spectrometry using a VG5400 equipped with an electron multiplier Balzers 217 SEV SEN coupled to an ion counter. Neutron fluence J for each sample is calculated using co-irradiated Alder Creek Sanidine (ACs-2) standard with an age of 1.193 Ma [START_REF] Nomade | Alder Creek sanidine (ACs-2), a Quaternary 40 Ar/ 39 Ar dating standard tied to the Cobb Mountain geomagnetic event[END_REF] and the total decay constant of [START_REF] Steiger | Subcommission on geochronology: convention on the use of decay constants in geo-and cosmochronology[END_REF]. For the irradiation 77, mean J-values computed from standard grains are J = 0.00024170 ± 0.00000145 for POL 13-01 and J = 0.00037885 ± 0.00000189 for POL 12-02 and for irradiation 66; J = 0.00036470 ± 0.00000182 and 0.00038070 ± 0.00000190 for POL 12-03; POL 12-01 respectively. Mass discrimination was estimated by analysis of Air pipette throughout the analytical period, and was relative to a 40 Ar/ 36 Ar ratio of 298.56 [START_REF] Lee | A redetermination of the isotopic abundances of atmospheric Ar[END_REF]. Procedural blank measurements are computed after every two or three unknown samples. For typical 10 min static blank, typical backgrounds are about 2.0-3.0 × 10 -17 and 5.0 to 6.0 × 10 -19 mol for 40 Ar and 36 Ar respectively. The precision and accuracy of the mass discrimination correction was monitored by weekly measurements of air argon of various beam sizes. Recent revisions of standards and decay constants suggest values of about ± 1% than the one we used (e.g. [START_REF] Kuiper | Synchronizing rock clocks of Earth history[END_REF][START_REF] Renne | Joint determination of 40 K decay constants and 40 Ar*/ 40 K for the Fish Canyon sanidine standard, and improved accuracy for 40 Ar/ 39 Ar geochronology. Response to the Comment[END_REF][START_REF] Phillips | Ultra-high precision 40 Ar/ 39 Ar ages for Fish Canyon Tuff and Alder Creek Rhyolite sanidine: new dating standards required? Geochim[END_REF][START_REF] Rivera | Age intercalibration of 40 Ar/ 39 Ar sanidine and chemically distinct U/Pb zircon populations from the Alder Creek Rhyolite Quaternary geochronology standard[END_REF], Jicha et al., 2016[START_REF] Niespolo | Intercalibration and age of the Alder Creek sanidine 40 Ar/ 39 Ar standard[END_REF]. However, the difference implied for the final ages obtained is here negligible, well within the full-propagated reported uncertainties.

ESR/U-series method

Seven bovid teeth (aurochs), recovered directly on the palaeosurface, were analysed both by ESR and U-series in order to estimate their age using ESR/U-series approach by US model [START_REF] Grün | ESR dating of tooth enamel: coupled correction for U-uptake and U-series disequilibrium[END_REF].

ESR measurements were performed on EMX Bruker ESR spectrometer using the following parameters: 10 mW microwave power, 0.1 mT modulation amplitude, room temperature, 10 mT scan range, 4 min scan time and 100 kHz frequency modulation, at least four measurements for each dose on different days. The ESR intensities were extracted from the g = 2.00018 enamel ESR signal through peak-to-peak (T1-B2) amplitude measurements according to [START_REF] Grün | Methods of dose determination using ESR spectra of tooth enamel[END_REF].

The teeth were prepared following the protocol proposed by [START_REF] Bahain | ESR and ESR/U-series dating study of several middle Palaeolithic sites of Pléneuf-Val-André (Brittany, France): Piégu, Les Vallées and Nantois[END_REF]. A part of an external enamel layer was extracted from each tooth; the enamel layer was then cleaned on each side by any contamination by sediment or dentine. After grounding and sieving, the 100-200 μm grain-size fraction was split into 10 aliquots. Nine of them were irradiated using 60 Co calibrated source (LNHB, CEA, CEN Saclay, France) at doses ranging from to 260 to 20,000 grays (Gy), then the ESR intensities I of the whole set of aliquots were measured using a Bruker EMX spectrometer. The equivalent doses D E were then extrapolated from the obtained dose growth curve using an exponential plus linear fitting function (E + L, according with [START_REF] Shao | The mathematical basis for the US-ESR dating method[END_REF] with a 1/I 2 weighting using Origin Pro 8.0 software. For La Polledrara samples, these D E are similar to those obtained with double saturation exponential function (DSE) generally preconized for high D E values [START_REF] Duval | Are published ESR dose assessments on fossil tooth enamel reliable?[END_REF], but with smaller associated uncertainties. U-series analyses were performed on each dental tissue by both gamma and alpha spectrometries (following the chemical protocol of [START_REF] Bischoff | A test of uranium-series dating of fossil tooth enamel: results from Tournal Cave, France[END_REF] in order to evaluate eventual radium and radon losses [START_REF] Bahain | ESR dating of tooth enamel: a comparison with K-Ar dating[END_REF] and to determine the U-uptake parameters necessary to the dose rate contributions and age calculations [START_REF] Shao | The mathematical basis for the US-ESR dating method[END_REF].

The beta dose contributions were corrected from the enamel part destroyed on each side of the enamel layer during the preparation process (according to [START_REF] Brennan | Beta doses in tooth enamel by "one Group" theory and the Rosy ESR dating software[END_REF] The radioelement contents of 10 sediment samples associated to the archaeological level were determined by gamma spectrometry and in situ gamma dose rate (5 measurements) was also measured using TL Al 2 O 3 dosimeters. The cosmic dose rate was estimated using the formula of [START_REF] Prescott | Cosmic ray contributions to dose rates for luminescence and ESR dating: large depths and long-term time variations[END_REF]. The following mean values were then used for any age calculation: U = 12.63 ± 0.35 ppm; Th = 47.10 ± 0.61 ppm; K = 1.27 ± 0.03%; D γ + cosm = 2716 ± 40 μ Gy/a. As the excavation was open since a long time and covered by a structure, it was not possible to directly measure reliable water contents from the sediments. A fixed value of 15 ± 5% was therefore assumed for the age calculations. Were also used the following parameters: a k-value (α efficiency) of 0.13 ± 0.02 [START_REF] Grün | An alpha irradiator for ESR dating[END_REF]; water content of 0 wt% in the enamel and 7 wt% in the dentine; conversion contentsdoses factors from [START_REF] Adamiec | Dose-rate conversion factors: update[END_REF]. The "USESR" computer program (Shao et al., 2012) was used for the age calculation.

Results

40 Ar/ 39 Ar on sanidines single grains

Full analytical details for individual crystals are given in the supplementary dataset. In Fig. 3 results are presented for each level as probability diagrams [START_REF] Deino | Single-crystal 40 Ar/ 39 Ar dating of the Olorgesailie Formation, Southern Kenya Rift[END_REF]. A homogeneous population is considered relevant when the weighted mean of these crystals has a probability fit ≥ 0.1. The weighted average ages are calculated using IsoPlot 3.0 [START_REF] Ludwig | Isoplot 3.0 a geochronological toolkit for Microsoft Excel[END_REF]) and given at 2σ (95% of probability) including J uncertainty throughout the text. The full-propagated uncertainties (including the total 40 K decay constant) are given between brackets with the statistical characteristics. Individual crystals results are presented in the supplementary dataset in tables S1 to S4. -POL 13-01 Eighteen sanidines were individually dated. This white volcanic deposit, characterized by a very homogenous granulometry, is a primary volcanic deposit, however it displays a bimodal probability diagram. The volcanic nature of this layer is attested, however as the sample was taken in a borehole, it is not determined if it corresponds to a pyroclastic-flow or to an air-fall deposit. Nevertheless, the homogeneity of the deposit and its lithology suggests that it may correspond to a primary fine ash fall. The main population (juvenile one) of crystals is made of fifteen on the eighteen measured crystals. The three oldest crystals are centred at an age around 433 ka (Fig. 3). The juvenile population of sanidine crystals gives a weighted mean age of 411 ± 5 ka (10 ka, MSWD = 0.3 and P = 1). The 40 Ar/ 36 Ar initial ratio given by the inverse isochron for this population is 295 ± 9 (2σ analytical uncertainties) equivalent within uncertainties to the atmospheric ratio of 298.56.

-POL 12-02

We dated fifteen sanidines extracted from the cross-laminated fluvial deposit (Fig. 3). As expected for reworked volcanic deposit the probability diagram is multimodal. The main population of sanidines is made of eight crystals centred at 400 ka. The youngest mode, composed of five crystals, allows the calculation of a mean age of 359 ± 6 ka (8 ka, MSWD = 0.8 and P = 0.5). Two older crystals are also highlighted in the probability diagram, dating respectively to 454 ± 7 ka and 471 ± 7 ka. Their presence underlines the presence of much older eruptions reworked within the layer. The inverse isochron calculated using these 5 crystals displays a low scattered and 40 Ar/ 36 Ar initial ratio of 249 ± 41 (2σ, analytical uncertainties). Even if this ratio is very imprecise it is still within uncertainties equivalent to the atmospheric ratio.

-POL 12-01 and 12-03 A total of twenty-nine crystals extracted from the white volcanic material blocks found in the archaeological level were measured for POL 12-01 and POL 12-03 samples (fifteen for POL 12-01 and fourteen for POL 12-03, Fig. 3.

We pooled the results obtained for the two samples in a single diagram, as separated results were within uncertainties equivalent (Fig. 3). The pumices displayed similar results with one main juvenile population including 23 of the 29 crystals dated (Fig. 3). The weighted mean age obtained for this juvenile population is 325 ± 2 ka (6 ka, MSWD = 0.7 and P = 0.9). The six xenocrysts are scattered between 350 ka and 450 ka (Fig. 3).

ESR/U-series method

The ESR/U-series data (calculated using US model), dose rate contribution and ages are displayed Table 2. Fig. 4 presents the U-uptake kinetics reconstructed from corresponding U-uptake p parameters for each tooth and associated modelled dose-contributions. The modelled Uincorporation timing indicates for all the analysed tissues a post-burial uptake, ranging from relatively early uptake (P-values comprised between -1.0 and -0.6 to recent uptake (P > 0). It leads mechanically to a relatively great impact of the environmental dose rate contribution (gamma plus cosmic) on the age calculation. In supplementary data are presented information allowing the reader's better comprehension: in Fig. S1, ESR growth curves of the Polledrara tooth enamel samples and corresponding (Exp + Lin) D E extrapolation for the 7 teeth are shown; In Table. S5, equivalent doses obtained for the Polledrara tooth samples using Exponential + Linear (E + L), Double Saturating Exponential (DSE) and Single Saturating Exponential (SSE) functions respectively are presented; Fig. S2, demonstrates the comparison of the equivalent doses obtained for the Polledrara tooth samples using Exponential + Linear (E + L) and Double Saturating Exponential (DSE) functions respectively. In Table S6 are displayed the radioelement contents of the Polledrara sediments samples determined by low background high purity γspectrometry. Table S7 shows the gamma dose rate measured by TL (α-Al2O3:C) dosimeters at La Polledrara (by courtesy of H. Valladas, LSCE, France). Finally, Fig. S3 represents the map of La Polledrara site with locations of the sampled teeth, sediments and dosimeters.

Sampl

Two groups of dates can be observed on the age density plot (Fig. 5). The first one (5 teeth), around 304 ± 25 ka, fits well with 40 Ar/ 39 Ar dates, while the second one, centred at 196 ± 25 ka, seems greatly underestimated. These two teeth correspond to those for which the earliest U-uptake reconstructions were obtained. Isochronous plot showing measured equivalent dose values vs internal doses modelled was therefore build for the La Polledrara teeth (Fig. 5). The teeth corresponding to the oldest group are highly correlated (R 2 > 0.99), indicating that the measured environmental dose rate seems geologically representative for them. The intercept of the obtained correlation line equation with the Y-axis provides then the part of the D E related to this external dose. By dividing this value by the environmental dose rate including the external beta dose rate related to the sediments, an age estimate of ca 320 ka is obtained. This estimate is close to the age of the oldest population and agrees with the 40 Ar/ 39 Ar date of the archaeological layer.

On the other hand, the two other teeth are completely out of the line. It could indicate for them an underestimation of the D E , which could be related to the presence of unstable components in the ESR spectrum (Joannes-Boyau and [START_REF] Joannes-Boyau | Decomposition of beta-ray induced ESR spectra of fossil tooth enamel[END_REF]. It could be also due to an inaccurate dosimetric reconstruction, in relation with a local change of the environmental dose rate caused by the relatively late U-uptake modelled for the whole set of samples, as evoked recently for teeth from another Italian Middle Pleistocene site, Isernia la Pineta, by [START_REF] Shao | Monte Carlo approach to calculate US-ESR age and age uncertainty for tooth enamel[END_REF].

Discussion

About the age of the archaeological remains

The 40 Ar/ 39 Ar method has yielded to the measurement of four different samples for the Polledrara belonging to three different stratigraphic levels (Fig. 2). The white volcanic layer that is a primary volcanic deposit, located below the site is dated to 411 ± 5 ka (9 ka) whereas the fluvial unit 1 m above, reworks several volcanic eruptions. The youngest one, that brings chronological information for the layer, is dated to 359 ± 6 ka (8 ka) (see Fig. 2, Fig. 3).

This date leads us to believe that this fluvial layer is younger than 359 ± 6 ka (8 ka) and encourages us to make a correlation with the phase occurred during glacial termination IV at the onset of MIS 9 that led to the Aurelia Formation deposition [START_REF] Anzidei | Ongoing research at the late Middle Pleistocene site of La Polledrara di Cecanibbio (central Italy), with emphasis on human elephant relationships[END_REF]. The results for POL 12-01 and POL 12-03 samples confirm the geological uniformity of the volcanic material blocks found in the archaeological deposit, suggesting a unique origin, as demonstrated, within uncertainties, by the same age (see Tables S1 to S4 in supplementary dataset) on both largest and thinnest pumices taken in two different locations. We combined the results for these two samples and obtained a pooled age of 325 ± 2 ka (6 ka) (twenty-three on twenty-nine crystals measured). This age should be thus considered, within uncertainties, close to the deposition of the entire layer. As a consequence, the archaeological remains and palaeontological assemblages found at the bottom of this volcano-derived horizon may be considered as well constrained by the age of sanidines extracted from the white blocks. The Palaeoloxodon antiquus skeletons trapped in anatomical articulation in the upper part of the deposit are probably slightly younger, but within uncertainties also dated around 325 ± 2 ka (6 ka). In conclusion, 40 Ar/ 39 Ar results refine the previous hypothesis that placed La Polledrara di Cecanibbio contemporaneous with the interglacial period of the MIS 9 [START_REF] Anzidei | Ongoing research at the late Middle Pleistocene site of La Polledrara di Cecanibbio (central Italy), with emphasis on human elephant relationships[END_REF]. We can now with confidence place the site occupation slightly after the MIS 9 interglacial optimum (see Fig. 6).

Fig. 6. a) 40 Ar/ 39 Ar and ESR/U-series chronological constraint obtained for La Polledrara di Cecanibbio in correlation with the estimated age at Torre in Pietra for the Acheulian archaeological level and at Castel di Guido [START_REF] Villa | The Acheulian and early Middle Paleolithic in Central Italy: stability and innovation[END_REF][START_REF] Michel | Datation ESR de dents d'aurochs du site Paléolithique inférieur de Castel di Guido (Italie)[END_REF]. Major volcanic eruptions of the Lazio (Colli Albani (CA) and Monti Sabatini volcanic district (SVD)) between 450 and 300 ka are correlated to the archaeological sections. CA: Pozzolane Nere (PN), Villa Senni sequence (VN). SVD: Tufi Stratificati Varicolori di La Storta (TVLS) and Tufo di Bracciano (TB) [START_REF] Karner | The history of the Monti Sabatini and Alban Hills volcanoes: groundwork for assessing volcanic-tectonic hazards for Rome[END_REF][START_REF] Sottili | Geochronology of the most recent activity in the Sabatini Volcanic District, Roman Province, central Italy[END_REF]. These results and eruptions are compared with the δ 18 O climatic curve of KC01b obtained by the analyses of N. Pachyderma dx foraminifera [START_REF] Capotondi | Central Mediterranean Mid-Pleistocene paleoclimatic variability and its association with global climate[END_REF]. b) Pollen diagram obtained by [START_REF] Sadori | Pollen-based paleoenvironmental and paleoclimatic change at Lake Ohrid (SE Europe) during the past 500 ka[END_REF] based on the analyses of the Ohrid Lake sequence (Macedonia and Albania), pinus excluded. c) Locations of the KC01b core site and Ohrid Lake.

Results obtained by ESR/U-series analyses on aurochs teeth are in agreement with the 40 Ar/ 39 Ar on single-crystals ages. A mean age of 304 ± 25 ka for five on seven teeth dated was obtained, supported by an isochronous age estimated around 320 ka (see Fig. 5). The two other teeth gave a mean age of 196 ± 25 ka probably due to problems on palaeodose determination or on the palaeodosimetric reconstruction. However, the 40 Ar/ 39 Ar and ESR/Useries results are complementary and reflect a chronological coherence in the geological deposition of the site, refining the age proposed by Anzidei et al., 2012 (i.e. 340-320 ka). We now with confidence propose that the fossiliferous level can be attributed to the end of MIS 9 (probably after the climatic optimum, Fig. 6). It is worth mentioning that the same chronological coherence between the ESR/U-series and 40 Ar/ 39 Ar dating methods was recently demonstrated for the archaeological site of Guado San Nicola (Molise, [START_REF] Pereira | Peretto. 40Ar/39Ar and ESR/U-series dates for Guado San Nicola, Middle Pleistocene key site at the Lower/Middle Palaeolithic transition in Italy[END_REF] underlying the pertinence of combining ESR/U-series and 40 Ar/ 39 Ar dating methods for precisely and accurately dating Middle Pleistocene sites.

Volcanic origins of the eruptions recorded

The Lazio during the Middle Pleistocene was subjected to intense and regular volcanism.

Several volcanoes, such as the Monti Sabatini, the Colli Albani, the Vico and the Vulsini complexes, were very active between 700 and 250 ka (e.g. [START_REF] Karner | The history of the Monti Sabatini and Alban Hills volcanoes: groundwork for assessing volcanic-tectonic hazards for Rome[END_REF][START_REF] Marra | The Alban Hills and Monti Sabatini volcanic products used in ancient Roman masonry (Italy): an integrated stratigraphic, archaeological, environmental and geochemical approach[END_REF], Marra et al., 2014) and may have led to the deposition of a significant amount of volcanic material in the Tiber delta during the Middle Pleistocene as evidenced by the compositional data of the PGS sequence [START_REF] Tentori | Sand compositional changes as a support for sequence-stratigraphic interpretation: the Middle-Upper Pleistocene to Holocene deposits of the Roman Basin (Rome, Italy)[END_REF]. La Polledrara di Cecanibbio is located in the marginal sector of the influence area of Sabatini volcanic district of the 1800 km 2 of the Sabatini Volcanic District (SVD) (Fig. 1), making this volcanic complex the most probable source for the volcanic material found in the site like previously suggesting by the presence of large sanidines crystals [START_REF] Conticelli | Petrology and geochemistry of the ultrapotassic rocks from the Sabatini Volcanic District, central Italy: the role of evolutionary processes in the genesis of variably enriched alkaline magmas[END_REF] and by the 87 Sr/ 86 Sr measurements obtained by [START_REF] Castorina | Geochemical and Sr/Nd isotopic characterization of Middle Pleistocene sediments from the paleontological site of La Polledrara di Cecanibbio (Sabatini Volcanic District, central Italy)[END_REF].

The new 40 Ar/ 39 Ar ages obtained in this study bring new and more precise chronological information. They contribute to refine the origin of the volcanic materials found in La Polledrara by making correlations with well-known eruptions from the Roman province.

About the white volcanic layer origin

Firstly, the age of 411 ± 5 ka (9 ka) for the white volcanic tuff located below the archaeological sequence is comparable chronologically to known eruptions coming both from the Monti Sabatini and Colli Albani volcanic districts. In fact, for example the "Tufi Stratificati Varicolori di La Storta" (TVLS), correspond to a corpus of Monti Sabatini volcanoes eruptions dated to 410 ± 2 ka [START_REF] Karner | The history of the Monti Sabatini and Alban Hills volcanoes: groundwork for assessing volcanic-tectonic hazards for Rome[END_REF]. This eruption could be the source of the white volcanic layer found 3 m below La Polledrara di Cecanibbio site (411 ± 5 ka (9 ka)).

Another possibility that deserves to be mentioned is the Pozzolane Nere (PN) eruption dated to 407 ± 8 ka [START_REF] Karner | The history of the Monti Sabatini and Alban Hills volcanoes: groundwork for assessing volcanic-tectonic hazards for Rome[END_REF], see Fig. 6). This volcanic event is also recorded 50 km Southeast from the site, at Fontana Ranuccio in the Frosinone province (Lazio)(S. Nomade, personal communication, Pereira et al. in prep). However, according to the known dispersion of this eruption it seems less probable that the Pozzolane Nere reached La Polledrara di Cecanibbio area.

It is also interesting to mention the fact the Vico volcano is also very close from the site and one of the most prominent eruptions for this volcano is the Vico α eruption dated to 412 ± 2 ka (Marra et al., 2014). Chronologically the age obtained at La Polledrara for this level is compatible (411 ± 5 ka (9 ka)) with the Vico α age. It is thus important not to overlook this possibility for the volcanic origin of the level.

Origin of the volcanic material contained in the cross-laminated fluvial deposit

The age of 359 ± 6 ka (8 ka) provided for the youngest sanidines population recorded inside the cross-bedded fluvial layer has also (within uncertainties) been identified on the nearby Middle Pleistocene site of Torre in Pietra (Fig. 1, Fig. 6). This site unlike La Polledrara di Cecanibbio presents typical Acheulian assemblages rich in handaxes (recently dated around 354 ± 7 ka, [START_REF] Villa | The Acheulian and early Middle Paleolithic in Central Italy: stability and innovation[END_REF]. However, we noticed that the palaeontological assemblage found in Torre in Pietra (level m) is almost equivalent to the assemblage highlighted at La Polledrara di Cecanibbio. These two ages are within uncertainty chronologically close to the "Villa-Senni eruptive sequence" (VS) of the Colli Albani, which correspond to several eruptions very close in age [START_REF] Karner | The history of the Monti Sabatini and Alban Hills volcanoes: groundwork for assessing volcanic-tectonic hazards for Rome[END_REF]. According to [START_REF] Marra | The Alban Hills and Monti Sabatini volcanic products used in ancient Roman masonry (Italy): an integrated stratigraphic, archaeological, environmental and geochemical approach[END_REF] this eruptive sequence is currently dated between 351 ± 4 ka and 366 ± 7 ka. Future 87 Sr/ 86 Sr analyses on clino-pyroxenes (Cpx) from these two sites as well from the VS sequence are necessary to confirm or not our hypothesis concerning the origin of the volcanic material found in these layers at La Polledrara di Cecanibbio and Torre in Pietra.

Origin of the volcanic material included into the archaeological layer

During the period around 325 ka only few eruptions from the Sabatini volcanic district have been identified [START_REF] Sottili | Geochronology of the most recent activity in the Sabatini Volcanic District, Roman Province, central Italy[END_REF][START_REF] Marra | The Alban Hills and Monti Sabatini volcanic products used in ancient Roman masonry (Italy): an integrated stratigraphic, archaeological, environmental and geochemical approach[END_REF], Marra et al., 2014). The main known eruption that could correspond to the age of the white volcanic material (blocks and pieces) embedded into the archaeological layer is the Tufo di Bracciano eruption characterized by its richness in white pumices that formed the Bracciano Lake located only 25 km North of the archaeological site (Fig. 1). The volcanic event was dated in 2010 by Sottili et al. and two different ages were proposed: 307 ± 5 ka and 316 ± 6 ka (95% of probability). The nature of this volcanic deposit and the published ages support the correlation with the white blocks embedded in the archaeological layer at La Polledrara.

About the climatostatigraphic position of La Polledrara di Cecanibbio

In Fig. 6 we reported the age obtained for the archaeological layer interpreted as the age of La Polledrara di Cecanibbio deposit. This age is compared to the δ 18 O variations obtained using planktonic foraminifera (N. Pachyderma dx) from the KC01B core [START_REF] Capotondi | Central Mediterranean Mid-Pleistocene paleoclimatic variability and its association with global climate[END_REF]. Human presence at La Polledrara occurred contemporaneously to the middle part of the interglacial stage 9 but as highlighted Fig. 6, after what is considered to be the interglacial optimum s.s. We tried to further refine the palaeo-environmental condition during this specific period in Mediterranean realm thanks to the recent pollens diagram provided by [START_REF] Sadori | Pollen-based paleoenvironmental and paleoclimatic change at Lake Ohrid (SE Europe) during the past 500 ka[END_REF] from the Ohrid Lake (Macedonia/Albania border). This record covers the last fifteen marine isotopic stages and confirms the presence of mainly arboreal taxa in Western Europe after the MIS 9 climatic optimum. This is in agreement with the faunal and microfauna assemblages of La Polledrara di Cecanibbio suggesting rather hot and humid conditions typical of interglacial environment [START_REF] Anzidei | Nouvelles données sur le gisement Pléistocène moyen de La Polledrara di Cecanibbio (Latium, Italie)[END_REF]. We would also like to notice that, even if this paleo-environmental record is not located in Italy, it remains the only continuous well-dated continental record in the Mediterranean realm for this time period. In fact, almost a dozen of tephras layers coming from Italian volcanic provinces, like the Pozzolane Rosse eruption (457 ± 2 ka, Fig. 6), are recorded in the Ohrid sequence [START_REF] Leicher | First tephrostratigraphic results of the DEEP site record from Lake Ohrid (Macedonia and Albania)[END_REF]. In Fig. 6, is indicated the recently proposed age for Torre in Pietra acheulian level m [START_REF] Villa | The Acheulian and early Middle Paleolithic in Central Italy: stability and innovation[END_REF] compared with the new age proposed for La Polledrara di Cecanibbio. This comparison suggests that level m of Torre in Pietra is slightly older (MIS10/MIS9) than La Polledrara di Cecanibbio (MIS 9). However, according to the Ohrid pollen data [START_REF] Sadori | Pollen-based paleoenvironmental and paleoclimatic change at Lake Ohrid (SE Europe) during the past 500 ka[END_REF] and δ 18 O climatic curve [START_REF] Capotondi | Central Mediterranean Mid-Pleistocene paleoclimatic variability and its association with global climate[END_REF] of the KC01B site, it seems that climatic conditions weren't dramatically different between these two sites; probably rather drier and colder at Torre in Pietra (Fig. 6). These climatic conditions are related to the beginning of the MIS 9 interglacial phase and, as said previously, to the early aggradationnal phase of the Aurelian formation linked to the Mediterranean Sea level rise in response to the improving of the climatic conditions at the end of MIS 10 [START_REF] Marra | Independent 40 Ar/ 39 Ar and 14 C age constraints on the last five glacial terminations from the aggradational successions of the Tiber River, Rome (Italy)[END_REF]. We also compare La Polledrara di Cecanibbio and Torre in Pietra to the proposed age for the neighbouring archaeological deposit of Castel di Guido. This site presents bones tools industries, and a similar paleontological assemblage. Unlike la Polledrara and Torre in Pietra and due to the large uncertainty on the age proposed for Castel di Guido makes any conclusion premature. In fact, no 40 Ar/ 39 Ar date is currently available for this site and the ESR/U-series ages obtained by [START_REF] Michel | Datation ESR de dents d'aurochs du site Paléolithique inférieur de Castel di Guido (Italie)[END_REF] (Fig. 6) on auroch teeth have displayed a large dispersion of ages between 327 and 260 ka. This time range is too large to currently discuss the chronological position of this site within the Aurelia formation.

Conclusion

For the first time, direct 40 Ar/ 39 Ar and ESR/U-series constraints were obtained for La Polledrara di Cecanibbio archaeological site. 40 Ar/ 39 Ar measurements on sanidines extracted from volcanic material blocks found within the archaeological deposit suggest a deposition age of 325 ± 6 ka. ESR/U-series analyses on 5 teeth highlighted a minimum age of 304 ± 25 ka, in agreement with the 40 Ar/ 39 Ar age. These results allowed us to place with confidence the hominin occupation as well as faunal record of La Polledrara di Cecanibbio during MIS 9 slightly after the interglacial optimum. Despite the fauna similarities, La Polledrara di Cecanibbio is younger that the nearby archaeological site of Torre in Pietra (i.e. acheulian level m MIS 10/MIS 9 transition).

Fig. 1 .

 1 Fig. 1. Geological map showing the location of La Polledrara di Cecanibbio and the neighbouring archaeological sites of Torre in Pietra, Casal de'Pazzi, Castel di Guido and Osteria moricone[START_REF] Villa | The Acheulian and early Middle Paleolithic in Central Italy: stability and innovation[END_REF][START_REF] Manzi | The Casal de'Pazzi archaic parietal : comparative analysis of new fossil evidence from the late Middle Pleistocene of Rome[END_REF][START_REF] Anzidei | Two Middle Pleistocene sites near Rome (Italy): La Polledrara di Cecanibbio and Rebibbia-Casal de Pazzi[END_REF][START_REF] Barbattini | Nuovo giacimento del Paleolitico inferiore in Agro Castel di Guido (Roma)[END_REF][START_REF] Saccà | Taphonomy of Palaeloxodon antiquus at Castel di Guido (Rome, Italy): proboscidean carcass exploitation in the Lower Palaeolithic[END_REF][START_REF] Ceruleo | The archaic Acheulean lithic industry of the Cretone basin (Latium, central Italy)[END_REF] and with the active volcanic complexes of the Middle Pleistocene[START_REF] Karner | The history of the Monti Sabatini and Alban Hills volcanoes: groundwork for assessing volcanic-tectonic hazards for Rome[END_REF][START_REF] Sottili | Geochronology of the most recent activity in the Sabatini Volcanic District, Roman Province, central Italy[END_REF][START_REF] Marra | The Alban Hills and Monti Sabatini volcanic products used in ancient Roman masonry (Italy): an integrated stratigraphic, archaeological, environmental and geochemical approach[END_REF].

Fig. 2

 2 Fig. 2. a) Schematic stratigraphy of La Polledrara di Cecanibbio highlighting the sampling positions for the 40 Ar/ 39 Ar and ESR/U-series dating. b) Photo highlighting the white volcanic block where sample 12-03 was collected. c) Photo demonstrating sample 12-01 and the crosslaminated sediments (sample 12-02)

Fig. 3 .

 3 Fig. 3. 40 Ar/ 39 Ar results for La Polledrara di Cecanibbio presented as probability diagrams. MSWD = Mean Square Weighted Deviation, P = Probability fit. For the archaeological layer two different samples were taken (POL 12-01 and POL 12-03) and combined in the same probability diagram.

Fig. 4 .

 4 Fig. 4. U-uptake kinetics and contributions to the dose rate modelled for teeth from La Polledrara di Cecanibbio, Lazio, Italy from p parameters determined by US-ESR dating approaches.

Fig. 5 .

 5 Fig. 5. Age density probability plots (top) and isochron curves (bottom) obtained for teeth from La Polledrara di Cecanibbio, Lazio, Italy. Analytical uncertainties are given with ± 1σ.

234 U/ 238 U 230 Th/ 232 Th 230 Th/ 234 U 222 Rn/ 230 Th

  (Table 1).

		mel		± 0.053
	Po2012-05	Dent ine Ena mel	273.00 ± 9.2 2 9.98 ± 0.28	1.239 ± 0.036 1.185 ± 0.023	97 88	0.633 ± 0.033 0.699 ± 0.033	0.533 0.557	1238 ± 1 55	109 ± 1 4	78 ± 10
	Po2012-	Dent ine	340.53 ± 11. 61	1.252 ± 0.034	> 100	0.503 ± 0.027	0.385	1339 ± 1	225 ± 2	155 ± 1
	06	Ena mel	8.92 ± 0.25	1.164 ± 0.024	> 100	0.679 ± 0.037	0.650	67	8	9
	Po2012-07	Dent ine Ena mel	396.22 ± 13. 70 5.72 ± 0.24	1.062 ± 0.030 1.473 ± 0.061	> 100 > 100	0.654 ± 0.035 0.724 ± 0.035	0.279 0.780	1376 ± 1 72	138 ± 1 7	75 ± 9
									Remov	Remov
									ed	ed
	Samples	Tiss ue	U content (ppm)					Initial thicknes s (μm)	thickne ss interna	thickne ss externa
									l side	l side
									(μm)	(μm)
	Po2012-01	Dent ine Ena mel	342.83 ± 9.1 2 9.89 ± 0.26	1.215 ± 0.008 1.131 ± 0.021	20 > 100	0.658 ± 0.030 0.760 ± 0.034	0.351 0.612	1270 ± 1 59	172 ± 2 1	32 ± 4
	Po2012-02	Dent ine Ena mel	294.18 ± 9.9 6 10.11 ± 0.33	1.172 ± 0.033 1.148 ± 0.039	48 13	0.617 ± 0.027 0.798 ± 0.039	0.395 1.000	1323 ± 1 65	116 ± 1 4	6 ± 1
	Po2012-03	Dent ine Ena mel	283.76 ± 8.8 1 23.52 ± 0.83	1.215 ± 0.031 1.153 ± 0.044	85 46	0.575 ± 0.025 0.629 ± 0.032	0.390 0.321	1124 ± 1 40	191 ± 2 4	86 ± 11
	Po2012-04	Dent ine Ena	326.73 ± 8.7 9 13.80 ± 0.49 1.387 1.209 ± 0.026	> 100 53	0.646 ± 0.026 0.704 ± 0.034	0.426 0.497	1394 ± 1 74	43 ± 5	114 ± 1 4

Table 1 .

 1 U-series data (α-spectrometry) and samples thicknesses determined on teeth from La Polledrara di Cecanibbio (Lazio, Italy). Analytical uncertainties are given with ± 1σ.

es Tissue D E (Gy) U uptake parameter p D a αintern al (μGy/a ) D a β (μGy/a) D a (γ + cosm) (μGy/a )

								D a total (μGy/a )	ESR/U-series ages US model (ka)
	Po2012 -01	Dentine Enamel	1664.92 ± 168.64	-0.3600± 0.1509 1779 ± 868 0.2803 ± 0.2477	708 ± 183	2716 ± 40	5203 ± 888	320 ± 44
	Po2012 -02	Dentine Enamel	1901.67 ± 104.66	-0.5926 ± 0.027 2691 ± 696 0.2210 ± 0.1719	1150 ± 212	2716 ± 40	655 ± 729	290 ± 28
	Po2012 -03	Dentine Enamel	1845.44 ± 140.61	0.2083 ± 0.2341 0.5801 ± 0.2872	2361 ± 487	1074 ± 52	2716 ± 40	6151 ± 702	300 ± 29
	Po2012 -04	Dentine Enamel	1717.57 ± 48.33	-0.6826 ± 0.1120 3008 ± 955 -0.5380 ± 0.1346	1902 ± 530	2716 ± 40	7626 ± 1093	183 ± 23
	Po2012 -05	Dentine Enamel	1420.99 ± 89.41	-0.0762 ± 0.0883 1472 ± 314 0.3044 ± 0.1143	1230 ± 200	2716 ± 40	5418 ± 375	317 ± 20
	Po2012 -06	Dentine Enamel	1499.71 ± 103.76	-0.1283 ± 0.1365 1388 ± 528 1.0761 ± 0.2634	863 ± 233	2716 ± 40	4968 ± 578	286 ± 28
	Po2012 -07	Dentine Enamel	1248.43 ± 34.97	-0.6405 ± 0.0680 1566 ± 338 -0.4890 ± 0.0836	1928 ± 360	2716 ± 40	6211 ± 495	201 ± 15

Table 2. Dose rates and ESR/U-series ages obtained on teeth from La Polledrara di Cecanibbio, Lazio, Italy. Analytical uncertainties are given with ± 1σ.

Acknowledgements

We would like to thank the ATM "Les dynamiques socio-ecosystèmiques, entre perturbations et résiliences environnementales et culturelles" of the Museum national d'Histoire naturelle of Paris (project "Acheulean and volcanism in Italy" conducted by M.H. Moncel (MNHN) and J.-J. Bahain (MNHN)) and the PHC Galileo project no. 28237WA "l'Acheuléen en Italie méridionale: Chronologie, Paleoanthropologie, Cultures' led by J.-J. Bahain (MNHN) and C. Peretto (Univ. of Ferrara) which allowed the funding of the sampling mission at La Polledrara di Cecanibbio and the "Ecole française de Rome" for A. Pereira's PhD support. We would like to extend our acknowledgments to Prof. S. Milli and M.R Palombo for their explanation about the geological context of the site as well as the two anonymous reviewers whose comments and suggestions improved the quality of this manuscript. This is LSCE contribution n° 6102.

Appendix A. Supplementary data

Supplementary material in annex


Olivier Podda

Laurent Tissandier

Annabelle Laplace-Ploquin

Etienne Deloule

Solubility of uranium oxide in ternary aluminosilicate glass melts

est destinée au dépôt

Solubility of uranium oxide in ternary aluminosilicate glass melts

Olivier Podda 1* , Laurent Tissandier 2 , Annabelle Laplace 1 , Etienne Deloule 2 1 CEA, DES, ISEC, DE2D, Laboratoire de Développement des Matrices de Conditionnement, Univ. Montpellier, Marcoule, France 2 Université de Lorraine, CNRS, CRPG, 54500 Vandoeuvre-lès-Nancy, France *olivier.podda@cea.fr The immobilization of highly radioactive waste using vitrification process has been in application since many decades [1]. This process can reduce the potential for radionuclides migration or dispersion [START_REF] Ojovan | An introduction to nuclear waste immobilisation[END_REF] by chemical incorporation into the structure of a glass matrix in order to trap radionuclides. This process is now under investigation for conditioning Intermediate Level Waste -Long Life (ILW-LL) using aluminosilicate glasses as host matrices. The vitrification must be able to maintain, within a certain range of composition and redox potential, the actinides solubility. It is known that uranium chemistry is complex in glass-forming systems due to the presence of many oxidation states (VI, V, IV), each of them having a specific solubility in melts. The aim of this work is to determine and model uranium solubility and its oxidation states as a function of the glass melt composition and oxidoreduction potential (oxygen fugacity, from 10 -0.7 atm to 10 -16 atm). The ternary SiO2-Al2O3-CaO (CAS) and SiO2-Al2O3-MgO (MAS) systems are studied. Different compositions are synthesized by modifying the Al content for each ternary system. Uranium is added in excess in order to reach an equilibrium between the melt and uranium oxide crystals.

(a) (b) Figure 1. Total uranium content reported as weight% UO2 as the function of oxygen fugacities for CAS system. Elaboration temperature was 1400°C. Error bars represent the standard deviation based on reproducibility of 30 EDS analyses for each samples. This presentation will give results on the behaviour of uranium over a large redox range. The results of uranium solubility (SEM/EDS) as a function of oxygen fugacity as well as a function of Al2O3 content will be presented (example on Figure 1). Analyses of uranium oxide crystals (XRD) were carried out. The proportion of uranium oxidation states was determined by XANES while their different structures were analysed by EXAFS. Hypotheses on the differences in behaviour between the two systems CAS and MAS will be formulated.


Valentina Lanza
email: valentina.lanza@univ-lehavre.fr

Edwige Dubos-Paillard
email: edwige.dubos-paillard@univ-paris1.fr

Rodolphe Charrier
email: rodolphe.charrier@univ-lehavre.fr

Nathalie Verdière
email: nathalie.verdiere@univ-lehavre.fr

Damienne Provitolo
email: damienne.provitolo@geoazur.unice.fr

Oscar Navarro
email: oscar.navarrocarrascal@univ-nantes.fr

Cyrille Bertelle
email: cyrille.bertelle@univ-lehavre.fr

Guillaume Cantin
email: guillaume-cantin@mail.com

Alexandre Berred
email: alexandre.berred@univ-lehavre.fr

Moulay A Aziz-Alaoui
email: aziz.alaoui@univ-lehavre.fr

Spatio-Temporal Dynamics of Human Behaviors During Disasters: A Mathematical and Geographical Approach

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

Introduction

The current major challenge in the field of populations safety and risk management is to progress in the understanding and ability to anticipate human behavior in face of complex threats and disasters of all origins. Several mathematical models of crowd dynamics, also in extreme scenarios as in a panic situation, have been proposed in literature (see the survey paper [START_REF] Bellomo | On the modeling of tra c and crowds: A survey of models, speculations, and perspectives[END_REF]). However, rare are the works that take into account several human behaviors at the same time and also transitions among these reactions [START_REF] Wang | Computational models and optimal control strategies for emotion contagion in the human population in emergencies[END_REF]. To meet this challenge, a consortium grouping searchers of di erent disciplines (mathematicians, geographers, psychologists, computer scientists) has been formed in the framework of the ANR project Com2SiCa. The aim of this research program is to understand and simulate human behaviors in areas a ected by disasters whatever their causes.The studied disasters are sudden, unexpected, without warning signs or with signs that are di cult to identify. A first work of this consortium proposed a fine analysis of human behaviors and their transitions according to the concerned brain areas [START_REF] Provitolo | Les comportements humains en situation de catastrophe: de l'observation à la modélisation conceptuelle et mathématique[END_REF][START_REF] Verdière | Mathematical modeling of human behaviors during catastrophic events[END_REF][START_REF] Cantin | Nonidentical coupled networks with a geographical model for human behaviors during catastrophic events[END_REF].

The work presented in this chapter considers a psychologically-based model describing human collective behaviors and emotional contagion in situation of natural, societal or technological disasters. Indeed, according to geographers, neuro-scientists and psychologists [START_REF] Provitolo | Emergent human behaviour during a disaster: Thematic versus complex systems approaches[END_REF][START_REF] Crocq | Paniques Collectives (Les)[END_REF], during a catastrophe, people scarcely stay in the same category of behavior during the all event. Moreover, imitation or social comparison is an important factor in the processes of behaviors changes [START_REF] Gilbert | When comparisons arise[END_REF].

Furthermore, the role played by the spatial configuration and the constraints introduced by the hazard (cutting of roads, destruction of buildings etc.) is not negligible in the dynamics of human reactions during a catastrophe. Indeed, mathematical models in literature [START_REF] Maury | A mathematical framework for a crowd motion model[END_REF][START_REF] Moussaïd | How simple rules determine pedestrian behavior and crowd disasters[END_REF] focus mainly on the influence of the spatial configuration (presence of obstacles or bottleneck formation, for instance) on the crowd flow dynamics, rather than on the crowd emotional states.

The aim of this chapter is to present a mathematical framework in order to have a spatial version of our model with a strong geographical meaning. In our approach, the space environment is modeled by a network that is adapted to the geographical area under study. The nodes represent a part of the geographical territory under study, with some properties and are filled with a group of individuals subject to the model behavior panel. The edges symbolize possible interactions between nodes. Each term in the network model is justified by geographical and/or psychological considerations. In particular, the coupling coe cients are here calculated using a physical and geographical approach and for each node of the network we introduce a capacity constraint [START_REF] Nicolis | Transition between segregation and aggregation: the role of environmental constraints[END_REF], that is the maximal number of individuals that each node can host. We show how, depending on these parameters, the network dynamics can change and di erent e ects, such as bottlenecks, can take place.

The chapter is organized as follows. Section 2 presents the a-spatial APC model. In Section 3, taking into account the geographical constraints, the network model is introduced. In Section 4 some numerical results for a network of three nodes are shown.

The aspatial behavioral model

Behaviors that can be observed during major disasters are non traditional. They are caused by hostile environmental pressure that imposes new ways of acting in a state of high or even extreme level of stress. They are conditioned by di erent parameters such as : -The types of hazards and anticipation of the beginning of the disaster: some disasters can be anticipated and announced by di erent information channels (newspapers, radio, televisions...). It is often the case of hurricanes, floods, volcanic eruption. However, other disasters as earthquakes and nuclear explosions are sudden. In the first case, we mainly observe controlled behaviors [START_REF] Baumann | Human response to the hurricane[END_REF][START_REF] George | Premieres impressions[END_REF] since the authorities' actions allow the population to face the danger (organized evacuation, consideration of the potential e ects of the disaster). In the second case, the reactions of the population are more instinctive [START_REF] Laborit | La légende des comportements[END_REF] and individualistic (freeze response or panic flight for example), at least during the first moments of the disaster [START_REF] Provitolo | Les comportements humains en situation de catastrophe: de l'observation à la modélisation conceptuelle et mathématique[END_REF].

-The location of individuals in relation to the disaster [START_REF] Crocq | Paniques Collectives (Les)[END_REF]. The a ected area is usually divided in four types of zones: the impact zone, where the material destructions, the number of casualties and the social and territorial disorganization are maximal; the destruction zone, where the material damages are very important, the social organization is very perturbed but the number of victims is less; and finally the marginal and external zones which are generally less impacted by the disaster.

-The temporality of the event which is at the origin of the disaster and the time of the day when it occurs. Many authors have proposed di erent stages to describe the course of a disaster. For example, W. Powell [START_REF] Powell | An introduction to the natural history of disaster[END_REF] distinguishes eight phases (predisaster, warming, threat, impact, inventory, rescue, remedy, recovery) as Henry W. Fischer [START_REF] Fischer | Response to disaster: Fact versus fiction & its perpetuation: The sociology of disaster[END_REF] proposes fives phases (pre-impact, impact, post-impact, recovery and reconstruction).

-The characteristics of the impacted zone: the human behaviors and associated displacements are generally constrained by the specificities of the territory. For example, the presence of open spaces or buildings permitting to ensure the security of populations, the number and the position of exits in buildings [START_REF] Helbing | Simulating dynamical features of escape panic[END_REF][START_REF] Henein | Macroscopic e ects of microscopic forces between agents in crowd models[END_REF] or the morphology of the network and its degree of deterioration [START_REF] Nabaa | Exploitation of a displacement survey to detect road network use vulnerability[END_REF] have an influence on people's reactions.

-The characteristics of individuals and the density of population: the behaviors vary with the physical characteristics of individuals (age, agility), their education and experiences (culture of risk). The local knowledge and the perception of the environment [START_REF] Wúermans | Modelling crowd dynamics, influence factors related to the probability of a riot[END_REF] are also important, as the familiarity with those present or the density of population. This density, which increases when the crowd is being formed, makes the situation more dangerous (i.e. reduction of the choices for the individual displacements, increasing of interactions between individuals and their neighbors) and can lead, for example, to extreme situations of trampling and su ocation.

These parameters highlight that for a same kind of disaster people's responses can be di erent. Moreover, during a disaster, individuals scarcely maintain the same behavior. We often observe a sequence of several behaviors (for example, freeze response followed by flight and containment). Nevertheless, we have few information on the evolution of population response. Indeed, it is unthinkable to continuously monitor each individual expecting a catastrophic event, or in the hope of avoiding one [START_REF] Provitolo | Les comportements humains en situation de catastrophe: de l'observation à la modélisation conceptuelle et mathématique[END_REF]. It is also impossible, from an ethical point of view, to voluntarily trigger a catastrophe to study the real observed behavior of populations in the face of danger. That's why the first step of approach consisted in building a first model to analyze the question of behavioral change.

This model, called APC (Alert-Panic-Control), relies on the point of view of psychologists. It is an extension of the PCR (Panic-Controlled-Reflex) model proposed in [START_REF] Verdière | Mathematical modeling of human behaviors during catastrophic events[END_REF][START_REF] Provitolo | Les comportements humains en situation de catastrophe: de l'observation à la modélisation conceptuelle et mathématique[END_REF] and studied in [START_REF] Cantin | Mathematical modeling of human behaviors during catastrophic events: stability and bifurcations[END_REF]. At our knowledge PCR model is the first SIR-based model in literature that aims to describe the dynamics of the multiple human collective behaviors in the scenario of a catastrophe. In the new model we are presenting here, human behavior are governed by two elements: the emotional charge that can be more or less strong according to the level of stress, and the emotional regulation, i.e. the ability of people to control emotional charge.

Taking into account the respective influence of these two elements, three main classes of behaviors are considered in the APC model:

i) The state of alert: people are on alert and in a situation of uncertainty. They are in search of information and try to identify the threat. They have often a low emotional charge and a strong emotional regulation. At the beginning of the catastrophe, all the people adopt an alert behavior that can last from few seconds to several minutes. ii) The state of panic: it corresponds to behaviors whose reasoning capacities are affected by a high level of stress. It gathers all automatic and uncontrolled behavior as freeze response, panic flight, automate behavior. In this state, the emotional charge is strong and is hardly regulated. This can lead to dangerous situations. That's why they must be quickly identified, not only they can disrupt the organization of relief, but also because they can endanger the lives of populations by pushing and running over people for example. These kinds of behaviors require a huge surge of nervous energy. So it often lasts at most one hour. iii)The state of control: the emotional charge is more or less intense but it can be regulated. As opposed to panic, people in a controlled behavior keep their selfcontrol and their cognitive functions (sense of reality, emotional control, danger assessment, ability to choose a solution). It gathers for example search for help, mutual aid, evacuation, looting, etc.

It is worth noting that in the description and analysis of these behaviors we do not judge the behaviors with respect to the event. A control behavior can be inappropriate while a panic one can be e cient. Here we are interested in understanding the behaviors themselves and the transitions from a behavior to another. Let us consider a population a ected by a catastrophic event. We will note C 0 the time at which the catastrophe takes place and for C C 0 , 0(C), ?(C), and 2(C) the number of individuals in a state of alert, panic and control, respectively. In addition, we note @(C) the number of individuals in the daily behaviors before the catastrophic event. In the same way we designate with 1(C) all the people that exit the impact zone. Furthermore, with respect to the previous model [START_REF] Provitolo | Les comportements humains en situation de catastrophe: de l'observation à la modélisation conceptuelle et mathématique[END_REF][START_REF] Cantin | Mathematical modeling of human behaviors during catastrophic events: stability and bifurcations[END_REF], deaths are taken into account in order to obtain a more realistic model. Thus, we note 3 (C) the individuals who lost their lives during the disaster.

It is well known that human beings rarely get stuck in a single type of reaction during a catastrophic event [START_REF] Crocq | Paniques Collectives (Les)[END_REF]. First of all, each individual experiences a behavioral evolution of his own. Typically, the behavior of the state of alert 0 is adopted as soon as the event is triggered, then people evolve towards the state of panic ? or the one of control 2, depending on their life experiences and risk education. The course of events can induce sometimes a new analysis of the situation and a temporary return to the alert state. Furthermore, imitation processes and social comparison are important factors that can induce transitions from one behavior to another one [START_REF] Gilbert | When comparisons arise[END_REF].

The scheme of the APC model can be found in Figure 1. Finally, the APC model equations are the following (C C 0 ):

daily W alert ⌫1 ⌫2 ⌫3 ⌫4 ⌧ panic control ⇠1 ⇠2 back to daily i ⇡2 ⇡? ⇡0 Fig. 1 APC model scheme § 0(C) = W(C)@(C) (⌫ 1 + ⌫ 2 + ⇡ 0 )0(C) + ⌫ 3 2(C) + ⌫ 4 ?(C) + (0(C), 2(C))0(C)2(C) + ⌧ (0(C), ?(C))0(C) ?(C), § 2(C) = ⌫ 1 0(C) + ⇠ 1 ?(C) (⌫ 3 + ⇠ 2 + ⇡ 2 )2(C) (0(C), 2(C))0(C)2(C) + (2(C), ?(C))2(C) ?(C) i(C)2(C), § ?(C) = ⌫ 2 0(C) + ⇠ 2 2(C) (⌫ 4 + ⇠ 1 + ⇡ ? ) ?(C) ⌧ (0(C), ?(C))0(C) ?(C) (2(C), ?(C))2(C) ?(C), (1)
§ @(C) = W(C)@(C), § 1(C) = i(C)2(C) § 3 (C) = ⇡ 0 0(C) + ⇡ 2 2(C) + ⇡ ? ?(C).
We note ⌫ 1 and ⌫ 2 the proportions of individuals who, at time C, naturally evolve from the state of alert to a controlled behavior and to the state of panic, respectively. The proportions corresponding to the comeback from the control behavior to the alert, and from the panic to the alert are noted ⌫ 3 and ⌫ 4 , respectively. The rates of transition from panic to control, and control to panic, are noted ⇠ 1 and ⇠ 2 , respectively. Coe cients ⇡ 0 , ⇡ ? and ⇡ 2 are the death rates of the three populations.

Since imitation processes can be similar to contagion ones, the imitation functions have been built using a SIR model approach and taking into account that the behavior of the majority influences the behavior of the minority. For example, for the imitation between alerted and controls, we have:

(0, 2)02 = U 1 b ⇣ 2 0 + Y ⌘ • 2 # • 0 + U 2 b ⇣ 0 2 + Y ⌘ 0 # • 2, (2)
where

b (B) = B 2 1 + B 2 , # = # (C) = @(C) + A (C) + ?(C) + 2(C) + 1(C) is the total population at time C, and Y << 1. B b (B)
Fig. 2 The graph of function b , which is involved in the modeling of the imitation terms.

In particular,

U 1 b ⇣ 2 0 + Y ⌘ • 0 # • 2
represents the proportion of population in alert behavior that become controlled by mimicking the controlled people around them. The term 2 #

is the classic "proportional incidence rate" found in many epidemic models [START_REF] Arino | Disease spread in metapopulations[END_REF][START_REF] Blackwood | An introduction to compartmental modeling for the budding infectious disease modeler[END_REF] which models the fact that each individual in the alert behavior does not meet all the people in the controlled behavior (this is impossible especially in the case of a dense crowd), but only a proportion of this sub-population. The term

U 1 b ⇣ 2 0 + Y ⌘
is the probability that an individual in the alert behavior becomes controlled. The b function models the fact that only if there is a majority of controlled people, alerted individuals adopt a controlled behavior. Similarly

U 2 b ⇣ 0 2 + Y ⌘ 0 # • 2
represents the fraction of individuals in a controlled behavior that mimics those in an alert behavior. Analogously, functions ⌧ and are defined as

8 > > > > > > < > > > > > > : ⌧ (0, ?)0? = V 1 b ⇣ ? 0 + Y ⌘ ? # • 0 + V 2 b ✓ 0 ? + Y ◆ 0 # • ? (2, ?)2? = W 1 b ⇣ ? 2 + Y ⌘ ? # • 2 + W 2 b ✓ 2 ? + Y ◆ 2 # • ?, (3)
Finally, the function W models the trigger of the catastrophe while the function i describes exit from the impact zone, that we suppose can be achieved only being in a controlled behavior. They are defined as

W(C) = Z (C, C 0 , C 1 ) and i(C) = Z (C, C 2 , C 3 ), C 2 R
where Z is defined as:

Z (C, g 0 , g 1 ) = 8 > > > > < > > > > : 0 if C < g 0 1 if C > g 1 1 2 1 2 cos ✓ C g 0 g 1 g 0 c ◆ si g 0  C  g 1 .
Table 1 sums up the notations of the APC model.

Remark 2.1

It is easy to notice that

8 C C 0 , § 0(C) + § 2(C) + § ?(C) + § @(C) + § 1(C) + § 3 (C) = 0.
The population under study is thus constant over time

8 C C 0 , 0(C) + 2(C) + ?(C) + @(C) + 1(C) + 3 (C) = 2BC
and we have the following relation:

8 C C 0 , § 0(C) + § 2(C) + § ?(C) + § @(C) + § 3 (C) = § 1(C).
This means that the 5th equation is a linear combination of the other equations of the model, so we can reduce our system to 5 equations in terms of the state variables D = [0, 2, ?, @, E] ) . ⇤

In the following, we suppose all the population in a daily behavior before the onset of the catastrophe, thus we consider as initial condition D 0 = (0, 0, 0, #, 0) ) .

A network of APC models

If the APC model makes it possible to reflect on the di erent behaviors that can occur depending on the characteristics of the disaster, risk culture and imitation phenomena, it remains a-spatial. However, the dynamics and movements observed during a disaster are also guided by territorial configurations (open/closed environment, network connectivity, street widths, presence of squares, etc.) and the alternatives they o er, particularly in terms of evacuation, flight and accessibility to refuge areas.

The network structure

In our modeling process we work at a mesoscopic scale and we adopt complex networks and metapopulations frameworks. We suppose to split the environment under study in several patches, that will become the nodes of our network. The network edges symbolize interactions between nodes.They can be of two types. They can depict population displacements. This paper is mainly focusing on the methodological choices made to represent this kind of interaction. In the short term, it will be completed by a second kind of relationships permitting the dissemination of information between spatially non contiguous nodes to take into account the exchange of information by mobile phone or SMS alert systems for example [START_REF] Dubos-Paillard | Cheminements géographiques, de la modélisation urbaine à l'analyse des perceptions du risque d'inondation[END_REF].

Fig. 3 From the spatial partition of the territory (Nice seafront in France) to the studied network

The model equations

Here are our main assumptions: i) we consider a network of = non-identical nodes; ii) the population of the network is constant (each node having its own victims and assuming that there are no individuals coming in or out of the network). On the other hand, the population will not be constant on each node; iii)each node : has a maximum carrying capacity, that is a maximum number of individuals # <0G : that can be received; iv)we consider only linear couplings, that is to say physical displacements. In addition, we suppose there is no behavioral transition during the transfer; v) the dead people and people in a daily behavior do not move. People in a state of alert hardly move.

In the following we note

• # 8 = # 8 (C) = @ 8 (C) + 0 8 (C) + ? 8 (C) + 2 8 (C) + 1 8 (C
) the total population of the 8-th node at time C; • N + (8) the out-neighbors set of node 8 (that is the nodes that are adjacent to node 8 and whose edge starts from 8) [START_REF] West | Introduction to graph theory[END_REF];

• N (8) the in-neighbors set of node 8 (that is the nodes that are adjacent to node 8 and whose edge comes into 8).

Then, the equations for the APC network model are the following (8 = 1, . . . , =):

8 > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > < > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > : 30 8 3C = W 8 @ 8 (⌫
> > > > > > > > > > > > > < > > > > > > > > > > > > > : 8 (0 8 , 2 8 ) = 1 # 8 ✓ U 8 1 b ✓ 2 8 0 8 + Y ◆ + U 8 2 b ✓ 0 8 2 8 + Y ◆◆ ⌧ 8 (0 8 , ? 8 ) = 1 # 8 ✓ V 8 1 b ✓ ? 8 0 8 + Y ◆ + V 8 2 b ✓ 0 8 ? 8 + Y ◆◆ 8 (2 8 , ? 8 ) = 1 # 8 ✓ W 8 1 b ✓ ? 8 2 8 + Y ◆ + W 8 2 b ✓ 2 8 ? 8 + Y ◆◆ . ( 5
)
Remark 3.1 According to our assumptions, we have capacity constraints on each node. This means that when the maximum capacity of one node is reached at time C, then this node cannot receive other population from the others nodes, so at time C the incoming flux for this node must be zero. This property is taken into account by the terms ✓

1 # 8 # <0G 8 ◆ 8 = 1, . . . , =.
It is worth notice that if we suppose, for instance, that at time C the node 8 is full (i.e.

# 8 (C) = # <0G 8
), we will have '

: 2N (8) ✓ 1 # 8 # <0G 8 ◆ [ 0 :8 = ' : 2N (8) ✓ 1 # 8 # <0G 8 ◆ [ ? :8 = ' : 2N (8) ✓ 1 # 8 # <0G 8 ◆ [ 2 :8 = 0,
thus there is no incoming flux for node 8. ⇤

Coupling coe cients

As we have said before, a link between two nodes of the network represents the fact that the population in one node can move to the other. The proportion of the population in a behavior state which moves from node 8 to node 9 is modeled by a linear coupling coe cient, [ 2 8 9 or [ ? 8 9 depending on the behavior under study, in the network mathematical model (4). We recall that, according to our hypotheses, panic and control behaviors are the only ones that can move.

One of the main issue is therefore to quantify this linear coupling between two given nodes, that is between two spatial zones, according to the geographical configuration of these zones. Our study has led to a specific formulation for this coupling, which depends on some quantities when one considers some population going from one given node to another:

• the width ! of the exit from one node to another;

• the average speed hEi of the population leaving the node under study (it is noteworthy that this quantity is computed here only with the horizontal components of speed vectors);

• the global surface ( of the node under study from whom population is leaving. Thus, coupling coe cients can be viewed as the analogous of mass flow rates. Figure 4 represents an example of two nodes. In this configuration we have

[ 12 = hEi! ( 1 .
To get this formula, we have to consider the following definition of this coupling coe cient, that is the proportion of people who leave the space per minute:

[ 12 = 1 # 1 3# 12 3C . ! ( 1 ( 2 node 1 node 2 [ 12
Fig. 4 The coupling coe cient value [ 12 depends on the global surface of node 1, on the width of the exit from node 1 to node 2, and on the average speed hE i of the population leaving node 1.

The quantity 3# 12 corresponds to the population quantity that goes through the exit per time unit 3C, that is 3# 12 = = 1 hEi! 3C, where = 1 is the population density on node 1. To finally get the result in terms of densities, we have to divide this number of people by the global number of people on node 1 (having a surface ( 1 ), that is

# 1 = = 1 ( 1 .
Finally this gives the expression of the coupling.

Remark 3.2

• hEi is the average speed but each behavior has its own average speed, that is the way why we have to consider

[ 0 12 , [ 2 12 , [ ? 12 ,
• in case of multiple exits from node 8 to node 9, we have multiple ! 8 , so we have multiple contribution for the calculation of the coupling coe cient. ⇤

Case study and numerical results

Here we are interested in the scenario of a tsunami on the French Riviera caused by a seismic event. The arrival time of the first wave would vary from 15 to 30 minutes [START_REF] Ioualalen | Tsunami mapping related to local earthquakes on the french-italian riviera (western mediterranean[END_REF]. This short time would make it di cult to alert and organize the evacuation of the population by public authorities. The impact zone under study is the seafront of Nice (France) [START_REF] Provitolo | Des modèles multiples pour l'étude des risques et catastrophes[END_REF]. In the following, let us consider a network of three nodes such as in Figure 5. We have selected three nodes that correspond to a small part of the beach (Node 1), a staircase that allows someone in node 1 to leave the beach (Node 2) and a part of the Promenade des Anglais (Node 3). The goal for people who are on the beach is to reach the Promenade des Anglais where they will be in security.

We consider this disaster to be unexpected due to a Ligurian fault rupture [START_REF] Larroque | Morphotectonic and fault-earthquake relationships along the northern ligurian margin (western mediterranean) based on high resolution, multibeam bathymetry and multichannel seismic-reflection profiles[END_REF], thus we use the following functions W 8 and i 8 :

W 8 (C) = W(C) = Z (C, 1, 3) and i 8 (C) = i(C) = Z (C, 70, 100), C 2 R,
with Z defined as: for g 0  C  g 1 , g 0 , C, g 1 2 R, The parameters have been chosen in order to model a tendency to adopt a panic behavior in nodes 1 and 2, since the first node is the one directly impacted by the catastrophe while in the second one the narrowness of the staircase could play an important role. As initial condition, we suppose all the population in the daily behavior before the catastrophe, distributed in the three nodes as following: @ 1 (0) = 300, @ 2 (0) = 5 and @ 3 (0) = 195, thus in node 1 we have 60% of the total population, in node 2 we have 1% and 39% in node 3, respectively. Finally, we have considered the same coupling coe cients for the di erent populations. Of course this is just a possible scenario and di erent values of the parameters can be considered. Throughout these simulations we have chosen the following color coding: the variables of node 1 are represented in black, those of node 2 in blue and the ones of node 3 are in green, respectively.

Furthermore, in the following we have considered two di erent values of # <0G 2 , the maximum capacity of node 2, in order to investigate its e ect on the global dynamics of the network. In the first scenario we have taken # <0G 2 = # = 500, the extreme case where node 2 can hold all the population. In the second one, we have supposed a capacity constraint on node 2 and put # <0G We can see that the stair capacity constraint has a great influence on the course of the event. While all the population has left the beach after 15 minutes in the first scenario, more than 130 people remain in danger after this period in the second one due to the inability to use the stairs that are overcrowded (# <0G 2 = 50). After 30 minutes about 50 people are still trapped on the beach. During these 15 minutes, the percentage of population in panic increases from 75% to 77%. These data are important because people who are still on the beach at these selected times will be a ected by the tsunami wave and could possibly loose their live. The e ect of the stair capacity on the evacuation dynamics of node 1 can be better observed if we look at the evacuation time of node 1, defined as

) 4E 02 = inf {C 2 ]0; )] | 0 1 (C) + ? 1 (C) + 2 1 (C) < 10% @ 1 (0)} .
In Figure 7, the evacuation time of node 1 as function of the maximum capacity of the middle node # <0G 2 is represented. According to the spatial configuration and the scenarios under study, with a stair maximal capacity of 50 individuals, it appears that to evacuate about 300 people from the beach by one stair we should multiply the stair capacity by two to evacuate in 30 minutes and by eight to evacuate in 15 minutes.

Conclusion

In this paper, we have adopted a complex network approach in order to take into account the spatial variable in the modeling and analysis of the dynamics of human behaviors during catastrophic events. As case study, we considered a scenario consisting in a tsunami on the French Riviera caused by a seismic event. In this type of events the population must quickly evacuate the beach because the estimated time before the arrival of the first wave vary from 15 to 30 minutes. Nevertheless, this evacuation depends on the capacity of the stairs that allow to leave the beach. To analyze this aspect, we have considered an elementary network made up of three nodes that correspond to a small part of the beach were 300 people are located at the beginning of the event, a staircase that allows to leave the beach and a part of the Promenade des Anglais, considered as safe. Two scenarios about the arrival timeline of the first tsunami wave have been studied (15 and 30 minutes). We have also distinguished a model without capacity constraint and another where the number of individuals in the staircase can not be larger than 50. The numerical simulations show that the capacity constraints on the nodes of the network influence the global dynamics of the model. Without any constraint, people can evacuate in 15 minutes whereas there is still more than one third of the population on the beach when we add a capacity constraint in the stairs (50 persons). 74% of them are in panic. After 30 minutes one in six people is still trapped on the beach and the panic reaches 77% of them. To allow a rapid evacuation (about 15 minutes) of about 300 people the stair capacity should be multiplied by eight. The next steps of this research is to take more into account the field reality, to analyze the necessary time to evacuate di erent number of people according to the number of stairs and the possibility to go toward another stair when one of them is overcrowded. We also want to introduce in the model a second kind of relationships between non adjacent nodes to build scenarios permitting the dissemination of information by mobile phone or SMS alert systems, since these kinds of exchange also have an influence on people behaviors during a disaster.

Fig. 6 2 : # <0G 2 = 2 =

 6222 Fig. 6 Time course of the three most important populations 0 (solid line), ? (dashed line), 2 (dotted line), in node 1 (a)-(d), node 2 (b)-(e) and node 3 (c)-(f), for two di erent values of # <0G 2 :

2 = 2 . 2 = 2 =

 2222 10%# = 50. In Figure 6 the time dynamics for the three populations 0 (solid line), ? (dashed line) and 2 (dotted line) of the three nodes are shown, for the two di erent values of # <0G In (a)-(b)-(c) we have the time courses for # <0G #, while in in (d)-(e)-(f) we have the results when we consider the capacity constraint on node 2 equal to # <0G 0.1# = 50.

Fig. 7

 7 Fig. 7 Evacuation time for node 1 as function of # <0G 2 .

Table 1

 1 Variables, functions and parameters of the APC model

	Variables	Notation
	Daily behavior before the catastrophe @ (C) Alert behavior 0 (C) Control behavior 2 (C) Panic behavior ? (C) Behavior outside the impact zone 1 (C)
	Functions	Notation
	Beginning of the catastrophe Leaving from the impact zone Imitation functions	W (C) i (C) , ⌧,
	Parameters	Notation
	Evolution from alert to control	⌫ 1
	Evolution from alert to panic	⌫ 2
	Evolution from control to alert	⌫ 3
	Evolution from panic to alert	⌫ 4
	Evolution from panic to control	⇠ 1
	Evolution from control to panic	⇠ 2
	Mortality rates	⇡ 0 , ⇡ ? , ⇡ 2
	Imitation from alert to control	U 1
	Imitation from control to alert	U 2
	Imitation from alert to panic	V 1
	Imitation from panic to alert	V 2
	Imitation from panic to control	W 1
	Imitation from control to panic	W 2

  8 1 + ⌫ 8 2 + ⇡ 8 0 )0 8 + ⌫ 8 3 2 8 + ⌫ 8 4 ? 8 + 8 (0 8 , 2 8 )0 8 2 8 + ⌧ 8 (0 8 , ? 8 )0 8 ? 8 , 2 8 )0 8 2 8 + 8 (2 8 , ? 8 )2 8 ? 8

		+	' : 2N (8)	✓	1	# 8 # <0G 8	◆	[ 0 :8 0 :	' : 2N + (8)	✓	1	# : : # <0G	◆	[ 0 8: 0 8 ,
	32 8 3C	= ⌫ 8 1 0 8 + ⇠ 8 1 ? 8 (⌫ 8 3 + ⇠ 8 2 + ⇡ 8 2 )2 8 8 (0 8 i 8 2 8 + ' : 2N (8) ✓ 1 # 8 # <0G 8 ◆ [ 2 :8 2 :	' : 2N + (8)	✓	1	# : : # <0G	◆	[ 2 8: 2 8 ,
	3? 8 3C	= ⌫ 8 2 0 8 + ⇠ 8 2 2 8 (⌫ 8 4 + ⇠ 8 1 + ⇡ 8 : 2N (8) ✓ 1 # 8 # <0G 8 ◆	[ ? :8 ? :	' : 2N + (8)	✓	1	# : : # <0G	◆	[ ? 8: ? 8 ,
	3@ 8	= W 8 @ 8 ,
	3C
	31 8	= i 8 2 8 ,
	3C
	3E 8 3C	= ⇡ 8 0 0 8 + ⇡ 8 2 2 8 + ⇡ 8 ? ? 8 ,									(4)
	with the dependencies on C being omitted to lighten notation and where
		8

? ) ? 8 ⌧ 8 (0 8 , ? 8 )0 8 ? 8 8 (2 8 , ? 8 )2 8 ? 8 + '

Acknowledgements This work has been supported by the French government, through the National Research Agency (ANR) under the Societal Challenge 9 "Freedom and security of Europe, its citizens and residents" with the reference number ANR-17-CE39-0008, co-financed by French Defence Procurement Agency (DGA) and The General Secretariat for Defence and National Security (SGDSN).

Fig. [START_REF] Cantin | Nonidentical coupled networks with a geographical model for human behaviors during catastrophic events[END_REF] The network under study.

Z (C, g 0 , g 1 ) =

8 > > > > < > > > > :

In the selected scenario, we have chosen the function W very sharp such that in three minutes the majority of the population in the daily behavior becomes alert. Furthermore, we suppose that people can exit from the impact zone only after 70 minutes from the beginning of the catastrophe. Table 2 shows the parameters values for the numerical simulations we will show in this paper. We remark that here the superscript denotes the node number, e.g. ⌫ 8 1 is the coe cient ⌫ 1 of the node 8.

Table 2 Parameters values for the numerical simulations

Parameters Values Parameters Values Parameters Values