Manuel Brazidec
email: manuel.brazidec@gmail.com

Vincent Perrichot
email: vincent.perrichot@univ-rennes1.fr

The first flat wasps (Hymenoptera: Bethylidae) from Miocene Mexican amber

Keywords: Insecta, Chrysidoidea, Bethylinae, Epyrinae, Scleroderminae, Chiapas amber, 1. Introduction

Despite a fairly good number of Miocene insect-bearing deposits available worldwide, the bethylid wasps from this period are yet very poorly known. Here, we describe and figure three new species in three subfamilies, from the early to middle Miocene of Totolapa (Mexico): Goniozus cotyi sp. nov. (Bethylinae), Bakeriella nanyhelae sp. nov. (Epyrinae), and Solepyris electromexicanus sp. nov. (Scleroderminae). The cosmopolitan Goniozus Förster, 1856 was already known from the Miocene of Dominican Republic, whereas the Pan-American Bakeriella Kieffer, 1910 and the South-American Solepyris Azevedo, 2006 are recorded for the first time as fossil. Our finding expands the geographical distribution of the latter genus much northward in the New World.

in tropical regions. Today the family comprises more than 2900 extant species that are mainly parasitoids of lepidopteran and coleopteran larvae [START_REF] Azevedo | Coleoptera: Curculionidae: Cossoninae) from Mexican amber[END_REF][START_REF] Evans | A synopsis of the American Bethylidae (Hymenoptera, Aculeata)[END_REF]. The diversity of bethylid wasps is also witnessed through geological times, with about 100 fossil species described, principally from the long-surveyed Baltic Eocene amber. But whereas it is often repeated that Cretaceous bethylids are poorly documented, Miocene representatives did not receive much attention either. This is particularly surprising when considering that highly fossiliferous deposits such as Dominican and Mexican amber have been studied for more than six decades (e.g., [START_REF] Sanderson | Amber with insect and plant inclusions from the Dominican Republic[END_REF][START_REF] Snyder | Fossil termites from Tertiary amber of Chiapas, Mexico (Isoptera)[END_REF]. In fact, only five species are known from the Miocene, all but one from the New World: Goniozus respectus Sorg, 1988 (Bethylinae), Anisepyris gradatus Sorg, 1988 (Epyrinae), Apenesia miki (Terayama, 2004) (Pristocerinae), and Alongatepyris pedrocai Colombo and Azevedo (in Colombo et al., 2022a) (Scleroderminae), from Dominican amber; Parascleroderma palaeosinica Brazidec and Perrichot, 2022 (Pristocerinae) from Chinese amber of Zhangpu; and Epyris deletus Brues, 1910 (Epyrinae) from rock-imprints of Florissant, USA. However, it is worth mentioning that the latter specimen was attributed to Epyris s.l., since many diagnostic features cannot be observed on the compression fossil (Brues, 1910: fig. 1). Another bethylid from Florissant was briefly characterized but not named [START_REF] Brues | Fossil parasitic and phytophagous Hymenoptera from, Colorado[END_REF], and an unnamed species of Goniozus Förster, 1856 was also figured from compression fossils of Rubielos de Mora, in Spain [START_REF] Peñalver-Mollá | Estudio tafonómico y paleoecológico de los insectos del Mioceno de Rubielos de Mora (Teruel)[END_REF]. In general, however, bethylids are poorly preserved and even rarely observed in sedimentary rocks, maybe due to the small size and fossorial habits of these wasps. As small insects frequently moving on bark, these are more prone to fossilization in tree resin [START_REF] Solórzano Kraemer | Arthropods in modern resin reveal if amber accurately recorded forest arthropod communities[END_REF]. The scant Miocene record of Bethylidae may therefore be particularly enriched by screening amber, notably that of poorly investigated deposits such as Totolapa (Mexico), or recently discovered deposits from New Zealand, [START_REF] Solórzano Kraemer | Entrapment bias of arthropods in Miocene amber revealed by trapping experiments in a tropical forest in Chiapas, Mexico[END_REF][START_REF] Schmidt | Amber inclusions from New Zealand[END_REF][START_REF] Bouju | A review of amber and copal occurrences in Africa and their paleontological significance[END_REF][START_REF] Wang | The mid-Miocene Zhangpu biota reveals an outstandingly rich rainforest biome in East Asia[END_REF].

Here, we propose three new species of Bethylidae from the Totolapa deposit, one of the earliest-known amber sites from Chiapas, Mexico [START_REF] Bryant | A recently discovered amber source near Totolapa, Chiapas, Mexico[END_REF]. This is the first report of the family from this site, the biota of which being still largely unknown [START_REF] Solórzano Kraemer | Mexican amber[END_REF]Coty and Nel, 2013;[START_REF] Durán-Ruiz | Ants from the Miocene Totolapa amber (Chiapas, Mexico), with the first record of the genus Forelius (Hymenoptera, Formicidae)[END_REF][START_REF] Ross | A catalogue of the collections of Mexican amber at the Natural History Museum, London and National Museums Scotland, Edinburgh, UK[END_REF].

Material and methods

The studied specimens are contained in three amber pieces originating from the Totolapa deposit, State of Chiapas, southwestern Mexico, more specifically from a mine owned by the Ramirez family along the Río Salado (see map in Durán-Ruiz et al., 2013: fig. 1). Ambers from Totolapa and Simojovel are chemically identical and have been assigned their own variety, the Simojovelite (Lambert et al., 1989;[START_REF] Riquelme | Amber from México: Coahuilite, Simojovelite and Bacalite[END_REF]. Furthermore, the amber-bearing strata in Totolapa have been correlated with the Mazantic shale and Balumtum sandstone from the Simojovel deposits, and are thus similarly dated as early-middle Miocene [START_REF] Perrilliat | Miocene mollusks from the Simojovel area in Chiapas, southwestern Mexico[END_REF][START_REF] Durán-Ruiz | Ants from the Miocene Totolapa amber (Chiapas, Mexico), with the first record of the genus Forelius (Hymenoptera, Formicidae)[END_REF][START_REF] Riquelme | Miocene spider Maevia eureka nov. sp. (Araneae: Salticidae)[END_REF]Hegna et al., 2020 and references therein). The pieces studied herein have been collected and bought to the mine owners in 2007 by M. David Coty (France) who recently offered them to one of us (M.B.) for study. We subsequently donated the specimens for permanent repository in the paleontological collection of the Museo de Paleontología de la Facultad de Ciencias (FCMP), Universidad Nacional Autónoma de México.

The amber pieces have been polished to facilitate the observation of the specimen, using thin silicon carbide sanding papers on a grinder polisher (Buehler EcoMet 30). The Simojovel examination and photographs were conducted with a Leica DMC4500 camera attached to a Leica M205C stereomicroscope. All images are digitally stacked photomicrographic composite of several focal planes, which were obtained using Helicon Focus 6.7. Adobe Illustrator CC2019 and Photoshop CC2019 software were used to compose the figures and ImageJ 1.53 for measurements [START_REF] Schneider | NIH Image to ImageJ: 25 years of image analysis[END_REF]. Details of the body have been redrawn digitally from sketch drawings made with a camera lucida attached to the stereomicroscope. The morphological nomenclature follows [START_REF] Lanes | Revisited morphology applied for Systematics of flat wasps (Hymenoptera, Bethylidae)[END_REF], except [START_REF] Harris | A glossary of surface sculpturing[END_REF] Material. Holotype number FCMP-1464, a complete male, with some features hidden by air bubbles.

Etymology. This species honours David Coty, for his generous donation of the specimen and in this way contributing to the knowledge of the Totolapa amber. The specific epithet is to be treated as a noun in a genitive case.

Diagnosis. (Male) Body stout; head wider than high (Fig. 1A); mandible thick, with four short teeth (Fig. 1C); flagellomeres slightly longer than wide; flagellomere 1 thinner than following ones; parapsidal signum deeply impressed (Fig. 1C); [1M] cell closed; prestigma triangular; pterostigma large, rounded; 2r-rs&Rs contiguous, only slightly arched toward anterior wing margin (Fig. 1D); femora enlarged; profemur largest, laterally flattened (Fig. 1B). Metasoma about as long as head + mesosoma combined, not distinctly pubescent (length 1.83 mm); petiole inconspicuous; segments subequal in length.

Systematic remarks. The specimen possesses numerous features reminiscent of the

Bethylinae, such as the thick mandibles with four teeth, the clypeal carina extending on the frons and outcurved as seen in profile, the tarsal claws strongly angled, the fore wing with Rs+M tubular and Rs&M widely angled, allowing attribution to this subfamily. Following the key of the bethyline genera of [START_REF] Azevedo | Coleoptera: Curculionidae: Cossoninae) from Mexican amber[END_REF], it keys in Goniozus for the following characters: antenna with 11 flagellomeres, dorsal pronotal area regularly long, fore wing with less than five closed cells, mesopleuron not prominent and fore wing with [2R1] cell opened.

It differs from Goniozus respectus, known from the more or less contemporary Dominican amber in having the 2r-rs&Rs vein shorter, not conspicuously angled apically, the cu-a vein arched (vs. straight) and the pterostigma more rounded (Sorg, 1988: fig. 22). It also differs from the unnamed Goniozus from compressions of Rubielos de Mora, Spain, in having the [1M] cell closed (but this might be due to the coarser preservation of rock-imprints), the pterostigma more rounded and the 2r-rs&Rs vein not angled apically (Peñalver-Mollá, 1998: fig. 36). Metasoma slightly longer than mesosoma, fusiform (length 2.91 mm); petiole inconspicuous; metasomal segments decreasing in length posteriorly; pubescence absent on anterior segments, long pubescence sparse but present on posterior segments; sting exerted, long (length 0.66 mm). Systematic remarks. Following the key to the subfamilies of Bethylidae of [START_REF] Azevedo | Coleoptera: Curculionidae: Cossoninae) from Mexican amber[END_REF], this specimen keys in the Epyrinae for the fully-developed wings, without Rs+M, the metanotum short, the metapectal-propodeal complex without posterior spines, the metasomal segment 2 regularly long, the mesopleuron with transepisternal line, the fore wing with anterior margin straight and C present. Following the key to the genera of Epyrinae of Colombo et al. (2022b), it keys between Epyris Kieffer, 1914 and Bakeriella Kieffer, 1910 for the mesoscuto-mesoscutellar foveae not connected by sulcus, the posterior ocelli broadly separated, the dorsal pronotal area without elevation anteriorly and the anterior margin not incurved, the anterior area of sternite 2 without flap and the antennae not pectinate, the mesoscuto-mesoscutellar foveae separated by less than half their own length, the metapectalpropodeal disc with distinct metapostnotal-propodeal carina. However, some features merely indicate Bakeriella for the present fossil: the body with metallic reflections, as is visible in some Bakeriella but not in Epyris [START_REF] Azevedo | Coleoptera: Curculionidae: Cossoninae) from Mexican amber[END_REF]; the mesoscuto-mesoscutellar foveae subelliptical rather than rectangular, a pattern of Bakeriella (e.g., Azevedo, 2014: figs. 1, 6, 9); the mesoscutellum not contacting the metapectal-propodeal complex, a diagnostic character of Bakeriella [START_REF] Azevedo | Synopsis of Bakeriella Kieffer, 1910 (Hymenoptera, Bethylidae)[END_REF]; and the strong metapostnotal-propodeal carina also merely indicates Bakeriella [START_REF] Azevedo | Synopsis of Bakeriella Kieffer, 1910 (Hymenoptera, Bethylidae)[END_REF][START_REF] Azevedo | Coleoptera: Curculionidae: Cossoninae) from Mexican amber[END_REF]. Following the key to the species of Bakeriella of [START_REF] Azevedo | Synopsis of Bakeriella Kieffer, 1910 (Hymenoptera, Bethylidae)[END_REF], the specimen keys between Bakeriella (Kieffer, 1910) and Bakeriella lindigi (Kieffer, 1910) for the dorsal pronotal area without carina, the mesoscuto-mesoscutellar foveae not connected, the median clypeal lobe angulate and the mesoscuto-mesoscutellar foveae wider than long. It differs from both species in having the notauli complete and the mandibles with three teeth. Therefore, we propose the new species Bakeriella nanyhelae sp. nov. for this specimen.

Subfamily Scleroderminae Kieffer, 1914

Genus Solepyris [START_REF] Azevedo | Two new genera of Sclerodermini (Hymenoptera: Bethylidae; Epyrinae) with large, scolebythid-like prosternums[END_REF] Solepyris electromexicanus sp. nov. Systematic remarks. Considering the general habitus and the large prosternum, our specimen could easily be mistaken for a Scolebythidae. But the reduced fore wing venation, the protrochanter inserted on apex of coxa instead of laterally, and the prosternum triangular rather than diamond-shaped, rather suggest that it belongs to the Scleroderminae. Following the keys to the Scleroderminae, our specimen keys in Solepyris Azevedo, 2006 for the antennae with 11 flagellomeres, the body much depressed with the eye as high as head laterally, the fore wing macropterous, the prosternum large, triangular and the vein A and Rs&M complete. The large prosternum is much uncommon within the Bethylidae and our specimen additionally shares numerous characters with Solepyris: the head wider than mesosoma, the clypeus short, the number of mandibular teeth, the notauli absent, the dorsal pronotal area depressed anteriorly with lateral margins incurved, the anteromesoscutum slightly overlapping posterolateral corners of pronotum, the Sc+R vein dilated distally, and the stigma absent. It differs from the two known species of the genus, S. unicus [START_REF] Azevedo | Two new genera of Sclerodermini (Hymenoptera: Bethylidae; Epyrinae) with large, scolebythid-like prosternums[END_REF]S. montuosus Azevedo, 2009, by the body more depressed, the femora more enlarged, and a different shape of the mandibles, with the dorsalmost tooth more basad [START_REF] Azevedo | A new species of Solepyris Azevedo (Hymenoptera, Bethylidae) from Brazil, with amended diagnosis of the genus[END_REF].

Discussion

Of the three species studied here, two belong to genera with a wide distribution: Gonozius, which is cosmopolitan, and Bakeriella, a Pan-American genus. Approximately thirty living species of Goniozus were recognized by [START_REF] Evans | The Bethylidae of America North of Mexico[END_REF] in Mexico. Judging by the presence of G. respectus in the more or less contemporary deposit of Dominican amber, its diversity was probably already settled by this epoch. This is supported by its presence in the fossil record since the Upper Eocene [START_REF] Ramos | Revision of Bethylinae fossils (Hymenoptera: Bethylidae) from Baltic, Rovno and Oise amber, with comments on the Tertiary fauna of the subfamily[END_REF]. It is therefore not surprising to record it in the Chiapas amber and demonstrates that Goniozus is well distributed around the globe since the Miocene at least. Similarly, [START_REF] Azevedo | Synopsis of Bakeriella Kieffer, 1910 (Hymenoptera, Bethylidae)[END_REF] records six extant species of Bakeriella in Mexico but Bakeriella nanyhelae sp. nov. is the first fossil of the genus. Given that Bethylidae from Mexican and Dominican ambers have been poorly investigated and that Bakeriella is almost restricted to the Neotropics, with a few species in Northern Mexico and the United States, this is not surprising. However, it denotes a long occurrence of both genera in the Neotropical region.

Solepyris is much more uncommon nowadays. The genus and type species S. unicus were erected by [START_REF] Azevedo | Two new genera of Sclerodermini (Hymenoptera: Bethylidae; Epyrinae) with large, scolebythid-like prosternums[END_REF] based on three females with a scolebythid-like habitus from Ecuador (Rio Palengue) and Brazil (Belo Horizonte). Later, [START_REF] Azevedo | A new species of Solepyris Azevedo (Hymenoptera, Bethylidae) from Brazil, with amended diagnosis of the genus[END_REF] found another species from Brazil (Espírito Santo) and investigated several sclerodermine collections but failed to find additional specimens. The few specimens collected showed that Solepyris might have a broad distribution throughout South America but our finding geographically expands it about 2,500 km northward in the Neotropics. However, the type specimens of S. unicus are distant of more than 4,000 km. Recently, Colombo et al. (2022a) proposed a hypothesis for the exclusive presence of strongly flattened sclerodermine wasps in tropical regions. They based it on the observation that Coleoptera larvae living in cryptic habitats, their hosts, occur widely in these regions. Unfortunately, nothing is known about the biology of Solepyris and none of the sclerodermine genera with such particular morphology listed in Colombo et al. (2022a) occur as north in Central America as Solepyris electromexicanus sp. nov. According to [START_REF] Azevedo | A new species of Solepyris Azevedo (Hymenoptera, Bethylidae) from Brazil, with amended diagnosis of the genus[END_REF] Cerambycidae; see [START_REF] Gupta | Biology and description of Megaprosternum cleonarovorum sp. nov. (Hymenoptera: Bethylidae) a gregarious larval ectoparasitoid of Cleonaria bicolor Thomson (Coleoptera: Cerambycidae) from India[END_REF]. It would have been possible for Solepyris electromexicanus sp. nov. to have a similar feeding habit since some Cerambycidae have been recorded emerging from Hymenaea tree [START_REF] Tavakilian | Neotropical tree species and their faunas of xylophagous longicorns (Coleoptera: Cerambycidae) in French Guiana[END_REF]. The Hymenaea genus is considered to be the producer of Chiapas amber [START_REF] Poinar | Hymenaea mexicana sp. nov. (Leguminosae: Caesalpinioidea) from Mexican amber indicates Old World connections[END_REF][START_REF] Solórzano Kraemer | Mexican amber[END_REF] and Cerambycidae are known from this deposit, but are yet undescribed (Ross et al., 2016: fig. 15). Further living observations and collection of additional specimens might help to better understand both the biology and biogeography of Solepyris.

The age of Totolapa amber has been widely debated since its discovery, because its geological settings could not have been studied precisely in situ. It was first thought to be Eocene, based on the geological map of the central depression region of Chiapas (INEGI, 1985), which would largely predate the other amber deposits of Mexico, dated late Oligocenemiddle Miocene. Lambert et al. (1989) contradicted this hypothesis by showing that ambers from Simojovel and Totolapa are chemically similar and hence likely from a same paleobotanical source. Further taxonomic studies of included arthropods (e.g Barrios-Izás and Coty, 2016;[START_REF] Coty | The first ant-termite syninclusion in amber with CT-scan analysis of taphonomy[END_REF][START_REF] Durán-Ruiz | Ants from the Miocene Totolapa amber (Chiapas, Mexico), with the first record of the genus Forelius (Hymenoptera, Formicidae)[END_REF][START_REF] Riquelme | Amber from México: Coahuilite, Simojovelite and Bacalite[END_REF]) revealed a paleofauna widely composed of extant genera of tropical to temperate affinities, which better correspond to a Miocene dating rather than Eocene. Our discovery of three modern genera of Bethylidae, of cosmopolitan or neotropical distribution, strengthens the proposal of a Miocene age for Totolapa amber.

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Genus

  Fig.1

  J o u r n a l P r e -p r o o f The J o u r n a l P r e -p r o o f The specific J o u r n a l P r e -p r o o f specific (Fig. J o u r n a l P r e -p r o o f (Fig. 1A) J o u r n a l P r e -p r o o f 1A); J o u r n a l P r e -p r o o f ; mandible J o u r n a l P r e -p r o o f mandible than J o u r n a l P r e -p r o o f than wide J o u r n a l P r e -p r o o f wide; J o u r n a l P r e -p r o o f ; flagellomere J o u r n a l P r e -p r o o f flagellomere impressed J o u r n a l P r e -p r o o f impressed (Fig. J o u r n a l P r e -p r o o f (Fig. 1 J o u r n a l P r e -p r o o f 1C J o u r n a l P r e -p r o o f C) J o u r n a l P r e -p r o o f ); J o u r n a l P r e -p r o o f ; [1M] J o u r n a l P r e -p r o o f [1M] Rs J o u r n a l P r e -p r o o f Rs contiguous, J o u r n a l P r e -p r o o f contiguous, enlarged J o u r n a l P r e -p r o o f enlarged; J o u r n a l P r e -p r o o f ; pro J o u r n a l P r e -p r o o f profemur J o u r n a l P r e -p r o o f femur Salado J o u r n a l P r e -p r o o f Salado Mine, J o u r n a l P r e -p r o o f Mine, Totolapa, J o u r n a l P r e -p r o o f Totolapa, middle J o u r n a l P r e -p r o o f middle Miocene, J o u r n a l P r e -p r o o f Miocene, Mesosoma with dorsum smooth (length 1.16 mm); propleuron not visible dorsally; dorsal pronotal area with lateral margin straight; anteromesoscutum as long as pronotum, parapsidal signum well impressed, notauli absent; scuto-scutellar suture without sulcus; mesopleuron not prominent. Fore wing macropterous, hyaline (LFW: 2.07 mm); C, Sc+R, M+Cu, A tubular; Rs&M curved; Rs+M tubular; [1M] cell (areolet) closed; prestigma triangular; pterostigma large, rounded; 2r-rs&Rs contiguous, slightly arched toward wing margin, distal segment absent. Legs pubescent; profemur largest, slightly flattened; meso and metafemora enlarged; tarsal claws curved.

  J o u r n a l P r e -p r o o f combined J o u r n a l P r e -p r o o f combined, J o u r n a l P r e -p r o o f , not J o u r n a l P r e -p r o o f not distinctly J o u r n a l P r e -p r o o f distinctly in J o u r n a l P r e -p r o o f in length J o u r n a l P r e -p r o o f length. J o u r n a l P r e -p r o o f . possesses J o u r n a l P r e -p r o o f possesses numerous J o u r n a l P r e -p r o o f numerous mandibles J o u r n a l P r e -p r o o f mandibles with J o u r n a l P r e -p r o o f with four J o u r n a l P r e -p r o o f four in J o u r n a l P r e -p r o o f in profile J o u r n a l P r e -p r o o f profile, J o u r n a l P r e -p r o o f , the J o u r n a l P r e -p r o o f the tarsal J o u r n a l P r e -p r o o f tarsal M J o u r n a l P r e -p r o o f M widely J o u r n a l P r e -p r o o f widely angled J o u r n a l P r e -p r o o f angled bethyline J o u r n a l P r e -p r o o f bethyline genera J o u r n a l P r e -p r o o f genera of J o u r n a l P r e -p r o o f of Azevedo J o u r n a l P r e -p r o o f Azevedo with J o u r n a l P r e -p r o o f with 11 J o u r n a l P r e -p r o o f Subfamily Epyrinae Kieffer, 1914 Genus Bakeriella Kieffer, 1910 Bakeriella nanyhelae sp. nov.

Fig. 2 LSID

 2 Fig.2

  J o u r n a l P r e -p r o o f Bethylidae J o u r n a l P r e -p r o o f Bethylidae of J o u r n a l P r e -p r o o f of Azevedo J o u r n a l P r e -p r o o f Azevedo developed J o u r n a l P r e -p r o o f developed wing J o u r n a l P r e -p r o o f wings, J o u r n a l P r e -p r o o f s, complex J o u r n a l P r e -p r o o f complex without J o u r n a l P r e -p r o o f without posterior J o u r n a l P r e -p r o o f posterior with J o u r n a l P r e -p r o o f with transepisternal J o u r n a l P r e -p r o o f transepisternal Following J o u r n a l P r e -p r o o f Following the J o u r n a l P r e -p r o o f the key J o u r n a l P r e -p r o o f key between J o u r n a l P r e -p r o o f between Epyris J o u r n a l P r e -p r o o f Epyris Kieffer, J o u r n a l P r e -p r o o f Kieffer, foveae J o u r n a l P r e -p r o o f foveae not J o u r n a l P r e -p r o o f not connected J o u r n a l P r e -p r o o f connected pronotal J o u r n a l P r e -p r o o f pronotal area J o u r n a l P r e -p r o o f area without J o u r n a l P r e -p r o o f without anterior J o u r n a l P r e -p r o o f anterior area J o u r n a l P r e -p r o o f area of J o u r n a l P r e -p r o o f of sternite J o u r n a l P r e -p r o o f sternite mesoscutellar J o u r n a l P r e -p r o o f mesoscutellar foveae J o u r n a l P r e -p r o o f foveae quinquepartita

Fig. 3 LSID

 3 Fig.3

  2.32 mm); venation reduced to Sc+R, Rs&M and A; Sc+R thickened distally, reaching anterior margin in basal half of wing. Hind wing without venation. Legs slightly pubescent; protrochanter originating from apex of procoxa; all femora swollen. J o u r n a l P r e -p r o o f glabrous J o u r n a l P r e -p r o o f glabrous forward J o u r n a l P r e -p r o o f forward; J o u r n a l P r e -p r o o f ; mandibles J o u r n a l P r e -p r o o fm andibles antennae J o u r n a l P r e -p r o o f antennae filiform J o u r n a l P r e -p r o o f filiform; J o u r n a l P r e -p r o o f ; scape J o u r n a l P r e -p r o o f scape wide J o u r n a l P r e -p r o o f wide (length J o u r n a l P r e -p r o o f (length ca. J o u r n a l P r e -p r o o f ca. ocellar J o u r n a l P r e -p r o o f ocellar triangle J o u r n a l P r e -p r o o f triangle compact J o u r n a l P r e -p r o o f compact carina J o u r n a l P r e -p r o o f carina present. J o u r n a l P r e -p r o o f present. coriaceous J o u r n a l P r e -p r o o f coriaceous (length J o u r n a l P r e -p r o o f (length 1.68 J o u r n a l P r e -p r o o f 1.68 rather J o u r n a l P r e -p r o o f rather angulate J o u r n a l P r e -p r o o f angulate; J o u r n a l P r e -p r o o f ; prosternum J o u r n a l P r e -p r o o f prosternum outcurved J o u r n a l P r e -p r o o f outcurved; J o u r n a l P r e -p r o o f ; dorsal J o u r n a l P r e -p r o o f dorsal incurved J o u r n a l P r e -p r o o f incurved, J o u r n a l P r e -p r o o f , posterior J o u r n a l P r e -p r o o f posterior anteromesoscutum J o u r n a l P r e -p r o o f anteromesoscutum Metasoma longer than mesosoma, fusiform, with denser pubescence on last segments (length 2.48 mm; height 0.32 mm); petiole inconspicuous; six tergites visible, subequal in length; no modifications of tergites; short sting visible.

  J o u r n a l P r e -p r o o f Scleroderminae. J o u r n a l P r e -p r o o f Scleroderminae. Solepyris J o u r n a l P r e -p r o o f Solepyris Azevedo, J o u r n a l P r e -p r o o f Azevedo, 2006 J o u r n a l P r e -p r o o f 2006 depressed J o u r n a l P r e -p r o o f depressed with J o u r n a l P r e -p r o o f with the J o u r n a l P r e -p r o o f the eye J o u r n a l P r e -p r o o f eye prosternum J o u r n a l P r e -p r o o f prosternum large J o u r n a l P r e -p r o o f large, J o u r n a l P r e -p r o o f , triangular J o u r n a l P r e -p r o o f triangular much J o u r n a l P r e -p r o o f much uncommon J o u r n a l P r e -p r o o f uncommon numerous J o u r n a l P r e -p r o o f numerous characters J o u r n a l P r e -p r o o f characters with J o u r n a l P r e -p r o o f with the J o u r n a l P r e -p r o o f the number J o u r n a l P r e -p r o o f number of J o u r n a l P r e -p r o o f of mandibular J o u r n a l P r e -p r o o f mandibular anteriorly J o u r n a l P r e -p r o o f anteriorly with J o u r n a l P r e -p r o o f with J o u r n a l P r e -p r o o f lateral J o u r n a l P r e -p r o o f lateral posterolateral J o u r n a l P r e -p r o o f posterolateral corners J o u r n a l P r e -p r o o f corners absent J o u r n a l P r e -p r o o f absent It J o u r n a l P r e -p r o o f It differs J o u r n a l P r e -p r o o f differs from J o u r n a l P r e -p r o o f from montuosus J o u r n a l P r e -p r o o f montuosus Azevedo, J o u r n a l P r e -p r o o f Azevedo,

,

  Solepyris might be closely related to Megaprosternum Azevedo, 2006, J o u r n a l P r e -p r o o f been J o u r n a l P r e -p r o o f been poorly J o u r n a l P r e -p r o o f poorly investigated J o u r n a l P r e -p r o o f investigated few J o u r n a l P r e -p r o o f few species J o u r n a l P r e -p r o o f species in J o u r n a l P r e -p r o o f in Northern J o u r n a l P r e -p r o o f Northern denotes J o u r n a l P r e -p r o o f denotes a J o u r n a l P r e -p r o o f a long J o u r n a l P r e -p r o o f long uncommon J o u r n a l P r e -p r o o f uncommon nowadays J o u r n a l P r e -p r o o f nowadays (2006) J o u r n a l P r e -p r o o f (2006) based J o u r n a l P r e -p r o o f based on J o u r n a l P r e -p r o o f on three J o u r n a l P r e -p r o o f three and J o u r n a l P r e -p r o o f and Brazil J o u r n a l P r e -p r o o f Brazil (Belo J o u r n a l P r e -p r o o f r n a l P r e -p r o o f (Espírito Santo) J o u r n a l P r e -p r o o f Santo) additional J o u r n a l P r e -p r o o f additional specimens J o u r n a l P r e -p r o o f specimens distribution J o u r n a l P r e -p r o o f distribution which has been reported to parasitise Cleonaria bicolor Thomson, 1864 (Coleoptera:

Acknowledgments

  J o u r n a l P r e -p r o o f biogeography J o u r n a l P r e -p r o o f biogeography of J o u r n a l P r e -p r o o f of Solepyris J o u r n a l P r e -p r o o f Solepyris debated J o u r n a l P r e -p r o o f debated since J o u r n a l P r e -p r o o f since its J o u r n a l P r e -p r o o f its discovery J o u r n a l P r e -p r o o f discovery precisely J o u r n a l P r e -p r o o f precisely in J o u r n a l P r e -p r o o f in situ J o u r n a l P r e -p r o o f situ central J o u r n a l P r e -p r o o f central depression J o u r n a l P r e -p r o o f depression the J o u r n a l P r e -p r o o f the other J o u r n a l P r e -p r o o f other amber J o u r n a l P r e -p r o o f amber deposits J o u r n a l P r e -p r o o f deposits (1989) J o u r n a l P r e -p r o o f (1989) contradicted J o u r n a l P r e -p r o o f contradicted Totolapa J o u r n a l P r e -p r o o f Totolapa are J o u r n a l P r e -p r o o f are chemically J o u r n a l P r e -p r o o f chemically source. J o u r n a l P r e -p r o o f source. Further J o u r n a l P r e -p r o o f Further taxonomic J o u r n a l P r e -p r o o f taxonomic Coty J o u r n a l P r e -p r o o f Coty et J o u r n a l P r e -p r o o f et al., J o u r n a l P r e -p r o o f al., 2014 J o u r n a l P r e -p r o o f 2014; J o u r n a l P r e -p r o o f ; composed J o u r n a l P r e -p r o o f composed J o u r n a l P r e -p r o o f gratitude J o u r n a l P r e -p r o o f gratitude manuscript. J o u r n a l P r e -p r o o f manuscript. This J o u r n a l P r e -p r o o f This work J o u r n a l P r e -p r o o f work greenhouses J o u r n a l P r e -p r o o f greenhouses on J o u r n a l P r e -p r o o f on the J o u r n a l P r e -p r o o f the diversification J o u r n a l P r e -p r o o f diversification new J o u r n a l P r e -p r o o f new genera J o u r n a l P r e -p r o o f genera of J o u r n a l P r e -p r o o f of large, J o u r n a l P r e -p r o o f large, scolebythid J o u r n a l P r e -p r o o f scolebythid 2009. J o u r n a l P r e -p r o o f 2009. A J o u r n a l P r e -p r o o f A new J o u r n a l P r e -p r o o f new J o u r n a l P r e -p r o o f from, J o u r n a l P r e -p r o o f from, Tertiary J o u r n a l P r e -p r o o f Tertiary of J o u r n a l P r e -p r o o f of Florissant J o u r n a l P r e -p r o o f Florissant 125. J o u r n a l P r e -p r o o f 125. 1983. A recently discovered amber source near Totolapa, Chiapas, Mexic J o u r n a l P r e -p r o o f 1983. A recently discovered amber source near Totolapa, Chiapas, Mexic E.E., J o u r n a l P r e -p r o o f E.E., Azevedo, J o u r n a l P r e -p r o o f Azevedo, C.O. J o u r n a l P r e -p r o o f C.O. (Hymenoptera, J o u r n a l P r e -p r o o f (Hymenoptera, Bethylidae), J o u r n a l P r e -p r o o f Bethylidae), amber. J o u r n a l P r e -p r o o f amber. Palaeoentomology J o u r n a l P r e -p r o o f Palaeoentomology J o u r n a l P r e -p r o o f https://doi.org/10.11646/palaeoentomology.5.1.6 J o u r n a l P r e -p r o o f https://doi.org/10.11646/palaeoentomology.5.1.6 J o u r n a l P r e -p r o o f 0166 J o u r n a l P r e -p r o o f 0166 (Hymenoptera, J o u r n a l P r e -p r o o f (Hymenoptera, Aculeata). J o u r n a l P r e -p r o o f Aculeata). North J o u r n a l P r e -p r o o f North of J o u r n a l P r e -p r o o f of Mexico. J o u r n a l P r e -p r o o f Mexico. Azevedo, J o u r n a l P r e -p r o o f Azevedo, C.O., J o u r n a l P r e -p r o o f C.O., 2017. J o u r n a l P r e -p r o o f 2017. Biology J o u r n a l P r e -p r o o f Biology egaprosternum cleonarovorum J o u r n a l P r e -p r o o f egaprosternum cleonarovorum sp. nov. (Hymenoptera: Bethylidae) a gregarious larval J o u r n a l P r e -p r o o f sp. nov. (Hymenoptera: Bethylidae) a gregarious larval Cleonaria bicolor J o u r n a l P r e -p r o o f Cleonaria bicolor Thomson (Coleoptera: Cerambycidae) from India. J o u r n a l P r e -p r o o f Thomson (Coleoptera: Cerambycidae) from India. Zootaxa 4237, 78 J o u r n a l P r e -p r o o f Zootaxa 4237, 78-J o u r n a l P r e -p r o o f -90. https://doi.org/10.11646/zootaxa.4237.1.4 J o u r n a l P r e -p r o o f 90. https://doi.org/10.11646/zootaxa.4237.1.4 1979. J o u r n a l P r e -p r o o f 1979. A J o u r n a l P r e -p r o o f A glossary J o u r n a l P r e -p r o o f glossary J o u r n a l P r e -p r o o f Estudio tafonómico y paleoecológico de los insectos del Mioceno J o u r n a l P r e -p r o o f Estudio tafonómico y paleoecológico de los insectos del Mioceno . Instituto de studios Turolenses J o u r n a l P r e -p r o o f . Instituto de studios Turolenses, Teruel, 179 p J o u r n a l P r e -p r o o f , Teruel, 179 p Miocene J o u r n a l P r e -p r o o f Miocene mollusks J o u r n a l P r e -p r o o f mollusks from J o u r n a l P r e -p r o o f from South J o u r n a l P r e -p r o o f South American J o u r n a l P r e -p r o o f American Earth J o u r n a l P r e -p r o o f Earth https://doi.org/10.1016/j.jsames.2010.04.005 J o u r n a l P r e -p r o o f https://doi.org/10.1016/j.jsames.2010.04.005 Hymenaea J o u r n a l P r e -p r o o f Hymenaea mexicana J o u r n a l P r e -p r o o f mexicana Mexican J o u r n a l P r e -p r o o f Mexican amber J o u r n a l P r e -p r o o f amber indica J o u r n a l P r e -p r o o f indica 139, J o u r n a l P r e -p r o o f 139, 125 J o u r n a l P r e -p r o o f 125-J o u r n a l P r e -p r o o f -132. J o u r n a l P r e -p r o o f 132. https://doi.org/10.1046/j.1095 J o u r n a l P r e -p r o o f https://doi.org/10.1046/j.1095 Perkovsky J o u r n a l P r e -p r o o f Perkovsky, J o u r n a l P r e -p r o o f , E.E., J o u r n a l P r e -p r o o f E.E., Rasnitsyn, J o u r n a l P r e -p r o o f Rasnitsyn, J o u r n a l P r e -p r o o f fossils (Hymenoptera: Bethylidae) from Baltic, Rovno and Oise amber, with comments on J o u r n a l P r e -p r o o f fossils (Hymenoptera: Bethylidae) from Baltic, Rovno and Oise amber, with comments on J o u r n a l P r e -p r o o f Maraun, M., J o u r n a l P r e -p r o o f M., Seyfullah, J o u r n a l P r e -p r o o f Seyfullah, L.J., J o u r n a l P r e -p r o o f L.J., Stebner, J o u r n a l P r e -p r o o f Stebner, from J o u r n a l P r e -p r o o f from New J o u r n a l P r e -p r o o f New Z J o u r n a l P r e -p r o o f Zealand. J o u r n a l P r e -p r o o f ealand. https://doi.org/10.1016/j.gr.2017.12.003 J o u r n a l P r e -p r o o f https://doi.org/10.1016/j.gr.2017.12.003 Eliceiri, J o u r n a l P r e -p r o o f Eliceiri, K.W., J o u r n a l P r e -p r o o f K.W., 2012. J o u r n a l P r e -p r o o f 2012. Methods J o u r n a l P r e -p r o o f Methods 9, J o u r n a l P r e -p r o o f 9, 671 J o u r n a l P r e -p r o o f 671-J o u r n a l P r e -p r o o f -675. J o u r n a l P r e -p r o o f 675. https://doi.org/10.1038/nmeth.2089 J o u r n a l P r e -p r o o f https://doi.org/10.1038/nmeth.2089 2010. J o u r n a l P r e -p r o o f 2010. Mexican J o u r n a l P r e -p r o o f Mexican major J o u r n a l P r e -p r o o f major world J o u r n a l P r e -p r o o f world deposits. J o u r n a l P r e -p r o o f deposits. Kraemer, J o u r n a l P r e -p r o o f Kraemer, M.M., J o u r n a l P r e -p r o o f M.M., Delclòs, J o u r n a l P r e -p r o o f Delclòs, J o u r n a l P r e -p r o o f 2018. J o u r n a l P r e -p r o o f 2018.

Figure 1 .Figure 2 .Figure 3 .

 123 Figure captions:

  CombinationType locality. Río Salado Mine, Totolapa, State of Chiapas, southwestern Mexico.

	Age. Early to middle Miocene, ca. 23-15 Ma
	Description. Body much depressed, elongate and poorly pubescent (length 5.05 mm). Head
	prognathous, ovoid, longer than wide; LH: 0.89 mm, WH: 0.76 mm; WF: 0.48 mm, HE: ca.
	0.19 mm; OOL: 0.43 mm; WOT: 0.08 mm; DAO: ca. 0.05 mm; VOL: 0.24 mm; frons flat;
	compound eyes elliptical, longer than high, as high as head laterally, glabrous, located
	anteriorly on head; clypeus with median lobe poorly projecting forward; mandibles rather
	long, with three teeth, ventralmost two teeth longest; antennae filiform; scape 2.3 times longer
	than pedicel; 11 flagellomeres slightly longer than wide (length ca. 0.09 mm); flagellomere 11
	longest; vertex convex with corner rounded; ocellar triangle compact, anterior ocellus
	posterior to supra ocular line; occipital carina present.
	Mesosoma with dorsum coriaceous (length 1.68 mm: height 0.44 mm); propleuron visible
	dorsally, anterior corner rather angulate; prosternum large, larger than procoxa, triangular
	with anterior margin outcurved; dorsal pronotal area elongate, depressed anteriorly, lateral
	margin strongly incurved, posterior margin slightly incurved with corners overlapped by
	anteromesoscutum; anteromesoscutum with parapsidal signum, without notauli; mesoscuto-
	mesoscutellar grooves elongate, separate by thin septum; mesoscutellum trapezoidal with
	blunt corners, large; metanotum barely visible; metapectal-propodeal complex smooth,
	without posterior spines; propodeal declivity short. Fore wing macropterous, hyaline (LFW:

We are in debt to David Coty for the generous donation of the material, discussion on the mining and geology of the deposit, and valuable comments on our work. We sincerely thank Manuel and Heriberto Ramirez, owners and miners of the Río Salado Mine, and their whole family for allowing David Coty's collecting on their property. We also thank Dr.

Francisco Sour Tovar (Universidad Nacional Autónoma de México) and Dr. Mónica M.

Solorzano-Kraemer (Senckenberg Research Institute, Germany), for advice and help with the final repository of the studied material. We finally express our gratitude to two anonymous reviewers for their comments on the first version of the manuscript. This work is part of Manuel Brazidec Ph.D. project on "The role of greenhouses on the diversification and evolution of chrysidoid wasps".


Sandra Bertezene

Managing health services according to the 'Complex Thought'

Keywords: conceptual, case study health establishments, complex thought, socio-economic management

Health establishments have to face and cope with an uncertain and turbulent environment in their management. They are asked at the same time to cut costs and to increase their social and economic performance. Their traditional way of managing is ill equipped to solve this conundrum. Their top-down management and compartmentalization of their organizational structure are not fit to have a global strategic and operational vision that can be embraced by all the actors of the organization and deployed effectively and efficiently. This paper proposes to develop a new type of management based on the 'Complex Thought' of Edgar Morin in order to be in a favourable position to improve the performance. The use of the Complex Thought can be operationalized thanks to the 'socio-economic' approach of Savall and Zardet. This conceptual framework has been tested by a case study of an establishment for dependent elderly person in France.

Findings:

The epistemological conditions of health establishments, as confirmed by the case study are not favourable to the use of the Complex Thought to set up a management system. However, the recourse to the socio-economic approach an its management tools can overcome, at least in part, this obstacle and permit to an auto-eco-re-organization, according to Morin's phrase, which offers opportunities for establishments to survive and develop in today's environment.

Introduction

Like most of OECD countries, France is trying to reduce its health expenses while meeting different challenges, which are all costly. They mainly deal with the following phenomena: the aging of the population and, correlated to it, the increase in diseases; from an organizational point of view, the integration of digitalization and the evolution of jobs that it implies. In this context, it is easy to understand that health establishments need to improve their performance while guaranteeing the quality of health care and the well-being of patients. A number of reforms have taken place over the last 30 years but without developing a continuous monitoring permitting to face an environment whose complexity is more and more felt, particularly since the apparition of the coronavirus.

The problematic here considered is that of the place of the 'Complex Thought' (hereafter 'CT') defined by Edgar Morin, in the monitoring of health organizations. Monitoring is here understood according to the definition of Lorino: 'A management approach linking strategy and operational actions' (Lorino, 2rthy, 1986). The hypothesis developed is the following: in a context constantly evolving, the lack of CT in the monitoring of establishments and services impacts their economic and social performance, which harms the quality of health care and the quality or professionals' working life.

Performance is a polysemic concept [START_REF] Bessire | Définir la performance[END_REF] which could be expressed in a nutshell as 'the ex post evaluation of the results obtained' (Bouquin, 1986, p. 114). This evaluation goes beyond the creation of value for customers and shareholders [START_REF] Chakravarthy | Measuring Strategic Performance[END_REF]. It concerns more widely the organizational performance [START_REF] Kaplan | The balanced scorecard-measures that drive performance[END_REF] centred on strategic objectives, their level of achievement and also how the actors organize themselves to attain these objectives. Consequently, the performance is not only seen in financial terms but also in qualitative and other quantitative terms [START_REF] Kaplan | The Balanced Scorecard: Translating Strategy into Action[END_REF] and leads us to consider everything that contributes to the attainment of the objectives [START_REF] Lorino | Méthodes et pratiques de la performance -Le guide du pilotage[END_REF]. The performance includes of course the financial measurement but concerns the whole monitoring [START_REF] Anthony | The management control function[END_REF]. It is with this logic that [START_REF] Savall | Maîtriser les coûts et les performances cachés, 7ème édition[END_REF] define the global performance of the organization, that is an approach which articulate the social performance and the economic performance starting from the principle that the competencies and all the other potentials offered by the human resources contribute to feed and augment the economic performance of organizations. This approach has been selected for this research as it offers a practical evaluation method of the performance and because it is adequate for the performance of health organizations (clinical quality, relevance of care, reaction capacity to expectations and needs of patients, productivity, etc.) [START_REF] Smith | Mesure des performances pour l'amélioration des systèmes de santé : expériences, défis et perspectives[END_REF][START_REF] Bertezene | Control of hospitals and nursing homes in France: The 2016 reform may indirectly improve a dysfunctional system[END_REF]. Each dimension offers elements of understanding of the health organization [START_REF] Sicotte | A conceptual framework for the analysis of health care organizations' performance[END_REF].

In order to explore this hypothesis, this article first presents the fundamental tenets of the CT of Edgar Morin (1), then the method for gathering and analyzing the data used to identify the place of the CT in the monitoring of health organizations (2). The results of the research are then presented (3), analyzed and discussed (4).

The Complex Thought of Edgar Morin as theoretical framework for the research

The CT [START_REF] Morin | Introduction à la pensée complexe[END_REF] links what is scattered and shows the solidarity between phenomena. It is actioned by an ethics of 'linkage' [START_REF] Le Moigne | Edgar Morin, le génie de la Reliance[END_REF], that is 'a essential ethical imperative which commands the other imperatives towards others, the community, society, mankind' (Morin, 2004, p. 114). The linkage achieves the connection between the elements, in a loop, and also a feedback loop. In this feedback loop, there is the production of new elements, called emergences (e.g. innovations, dysfunctions). These emergences are at the origin of the complexity, of open and living systems which reproduce themselves. For this linkage, 'linkage operators' are required. [START_REF] Morin | Quelle Université pour demain ? Vers une évolution transdisciplinaire de l'Université[END_REF] identifies four of them: the system as such, and the recursive, the dialogic and the hologrammatic principles.

1.1

The system

A health organization adopting a monitoring according to the CT is seen as a system, that is a relation between parts which are different one from another but which constitute an organized whole. According to the principle of linkage, the systems connects the parts to a whole, which can be more or less than the addition of its parts. New properties and attributes appear (the emergences) deriving from the very organization of these parts in a whole. These emergences cannot be reduced to the elements of the system that produces them and they act retroactively on these elements (feedback loop). Therefore, the establishment is not the mere addition of budgets, competencies, materials and premises. It is a locus of value creation, of practices and production of tacit and explicit knowledge which impact it endlessly. This systemic dimension of the organization is summed up in what [START_REF] Morin | La Méthode, Tome 2 -La vie de la vie[END_REF] calls the 'autoeco-re-organization' making an open and living system of a health service, able to adapt to and evolve in a volatile, uncertain, complex and ambiguous environment, as is the case today (Le Moigne, 1999).

The recursive, dialogic and hologrammatic principles

A monitoring according to the CT takes into consideration these three principles.

A process is recursive when the result of the process impacts it beginning. 'A recursive process is a process where the products and effects are at the same time the causes and the producers of what is produced' (Morin, 2005, p. 99-100). The establishment is the result of interactions between its actors (management, personnel, residents, etc.) and the establishment retroacts on these actors. This recursion is for example expected in the approaches of continuous improvement of quality implemented in establishments.

The dialogic principle 'can be defined as the complex association (complementary / competing / antagonistic) of instances which are all necessary for the existence, functioning and development of an organized phenomenon (Morin, 1986, p. 98). The association of complementary, and even of antagonistic, elements is at the heart of the monitoring of health organizations.

The hologrammatic principle implies that 'the whole is in a certain way (ingrained) in the part that is included in the whole. The complex organization of the whole (holos) requires the inscription ('ingrainment') of the whole (hologram) in each of its parts, yet distinct; thus, the organizational complexity of the whole requires the organizational complexity of the parts, which in its turn recursively requires the organizational complexity of the whole' (Morin, 1986, p. 112). For example, the deployment of the strategic project by the management among the personnel enables everyone to be engrossed with the medium-long term vision and to implement it operationally in the short term.

To sum up, the CT permits the 'auto-eco-re-organization' that the system needs to ensure its social performance which the source of the satisfaction of the actors of the organization and its economic performance reflecting the short and long term use of the resources of the organization [START_REF] Savall | Maîtriser les coûts et les performances cachés, 7ème édition[END_REF]. These two facets of performance are necessary for the development of the system, or its mere survival, which is threatened by the turbulences of the environment such as those caused by a sanitary crisis.

Methodology of identification of the place of the CT in the monitoring of health organizations: the socio-economic diagnostic

This research relies on an exploratory case study. The experimentation field is a home for dependent elderly people part of an associative group with 80 rooms and 55 staff.

The socio-economic theory [START_REF] Savall | Libérer les performances cachées des entreprises par un management socio-économique[END_REF][START_REF] Savall | Maîtriser les coûts et les performances cachés, 7ème édition[END_REF] proposes to evaluate the hidden costs and performances generated by the dysfunctions of the organization. They are called hidden because they cannot be identified in the classic accounting documents. In our present case, the dysfunctions, and their economic impact, linked to the absence of CT are identified thanks to a socio-economic diagnostic.

The diagnostic starts with the identification and the qualitative analysis of the non-quality and non-efficient zones in the establishments. Then follows an evaluation of the regulations in quantitative and financial terms. Data are collected in three complementary ways: observation, study of internal documents, interviews.

The first phase of interviews consists in the identification of the difficulties experiences by the actors because of the lack of CT in the monitoring of the organizations thanks to individual and semi-collective interviews. In order to understand the obstacles to the auto-eco-reorganization of the system, the interviews were led thanks to guide based on the essential three principles of the linkage: the recursive, dialogic and hologrammatic principles. Each principle is made of sub-themes proposed by the socio-economic diagnostic: working conditions, organization of work, communication-coordination-concertation, management of integrated training time and strategic implementation.

After this phase, a second series of directive interviews with a part of the management permitted to collect information about the regulation of the dysfunctions in terms of extratime (waste of time to ensure the regulation of the dysfunctions), of non-production (absence of activity due to a dysfunction), of over-consumption (unnecessary consumption of products), of over-compensation (salary gap between a higher paid person performing a task that should have been done by another person), and of creation of non-potential (cost of immaterial investments that cannot take place because the personnel is busy with regulating dysfunctions). These five components illustrate the economic impact of the regulation of dysfunctions. The dysfunctions are grouped into five indicators: absenteeism, personnel turnover, labour accidents (social indicators), quality defects and variances of direct productivity (economic indicators). Thanks to the evaluation of the hidden costs, it is possible to show the level of performance of the organization and to measure the gap with the level of performance expected. It is then possible to elaborate and implement solutions to improve the global performance.

A non-participating observation permitted to weigh certain dysfunctions and better understand certain regulations inside different services. The study of internal documents permitted to better understand the nature and the impacts of the dysfunctions.

The diagnostic can be summed up in the following way: identify the dysfunctions, evaluate quantitatively and financially the regulations implemented, and evidencing the waste of resources due to the lack of CT in the monitoring.

The results of the research: costly dysfunctions and harmful emergences for the auto-eco-re-organization

This section presents the results by pointing to the main obstacles to the auto-eco-reorganization in the light of the dialogic, hologrammatic and recursive principles. It ends with a global summary evaluation of the impact on the performance.

The dialogic principle

We recall that this principle consists in overcoming the contradiction caused by the conjunction of antagonistic elements.

The dialogic element (variety of professional cultures / unicity of the group culture) is not monitored. Due to insufficient communication between different groups with diverging goals and preoccupation, these groups of actors do not understand one another. The absence of dialogic relationships between centralization and decentralization, and verticality and networking is particularly underlined by the professionals. The centralization around the headquarters is privileged to the detriment of the decentralization in the establishments. Consequently it frequently happens that the directives given by the headquarters are not in adequacy with the expectations or needs of the teams, which creates tensions and dysfunctions.

Following the same logic, vertical relationships supersede networking. Multi-lateral relationships between establishments to created a network, are not encouraged. The only recognized relationships are bi-lateral and vertical, and essentially top-down between the headquarters and the establishment.

So, the management of different establishments has got the feeling that they are facing the same problems but do not have the opportunity to share their experiences and knowledge, and capitalize on them.

The hologrammatic principle

The hologrammatic principle teaches us that the whole is in the part, and the part is in the whole.

The values defined by the top management (solidarity, common life, quality of life) support the strategic project of the group and feed the projects of the establishments. These values are supposed to be spread throughout the establishment from the top to the bottom. To encourage this appropriation, these values are the object of different strategic and operational actions.

In spite of the efforts of the top management of the group, the 'whole', notably represented by these values, does not succeed in being 'ingrained' in the 'parts'. The obstacles to the hologrammatic principle inside the establishment are many. For example, to start with, the strategy of the group is not relayed and spread by the director of the establishment among the teams. The actions of communication do not then produce effects. The values are not appropriated by the teams to translate them into objectives and then concrete operations. In fact most of the personnel do not know these fundamental values as well as the project of the service which is supposed to guide everyday professional practices and behaviours. The personnel rejects the actions planned as they do not understand them.

The recursive principle

According to this principle, actions produce consequences that interact with the actions; the process is recursive when its result influences its beginning.

The top management has defined and formalized three strategic axes for the group to enable each establishment to translate the values into concrete actions: develop the various kinds of knowledge and a common sense of responsibilities with a concern for mutual commitment aiming at developing continuously the comfort and well-being of the elderly persons. These three axes deployed in the approach of continuous improvement of quality are supposed to ensure a sufficiently robust recursivity to trigger a virtuous loop inside the establishments. However, the interviews reveal a different reality due to three major problems.

First of all, many training periods are followed by the personnel without the new knowledge being implemented by the residents. It is then difficult to inscribe the quality of life of residents in a positive loop.

Second, the improvement of the care of residents is impeded par the lack of equipment. The result of the process of quality improvement does not influence positively its beginning.

Third, everyone works in their silos, isolated from the others, which makes it difficult to understand the expectations and needs of each actor.

These three problems impedes the quality of care, both medical and social, of the elderly persons.

A thwarted auto-eco-re-organization and a degraded performance

The lack of common work to progress collectively is flagrant. People meet too rarely to exchange information that could help in the quality of care, to think about solutions together and of course to innovate. Teams have difficulties in appropriating procedures and protocols written by people from the headquarters and by administrators who are far from them geographically, organizationally and culturally. This explains, at least in part, that these documents are little known and become obsolete without anybody noticing it.

Each service operates in its zone of competencies and prerogatives. Consequently the actors have very few opportunities to take the complexity of the internal and external environment into account. Practices can hardly evolve, progress and translate the strategic axes into actions because of the number of dysfunctions.

To sum up, the lack of autonomy and sense of responsibility of the teams, including the management of the establishment, generates dysfunctions which prevent the auto-ecore-organization from taking place.

Analysis and discussion: epistemological conditions not favorable for a monitoring through the Complex Thought counterbalanced by an engineering of the socio-economic management

This last part tries to show the fertile articulation between the Complex Thought and the socio-economic management.

Complex Though and socio-economic management: an epistemological articulation

One of the main reasons that can explain the lack of understanding of the Complex Thought, is epistemological. The cartesian thought with that of Aristotle leads to an analytical model of the construction of knowledge (Le Moigne, 2012) which consists in decomposing the subject studied. The analytical method aims at describing and explaining reality and at revealing its laws. Auguste [START_REF] Comte | Cours de philosophie positive[END_REF] proposes a classification of sciences, of which academic disciplines are the heirs, on this basis. This notably explains the compartmentalization of health professionals in contradiction with a context where changes and practices can only be trans-disciplinary and multi-professional [START_REF] Danan | De la nécessité d'innover à l'émergence de pratiques innovantes en santé[END_REF]. Descartes' principles have had useful consequences in the specialization of knowledge, but they have impeded any global view, any complex view [START_REF] Morin | Conférence inaugurale prononcée au Congrès mondial pour la pensée complexe[END_REF].

The socio-economic management [START_REF] Savall | Tétranormalisation : défis et dynamiques[END_REF][START_REF] Zardet | Becoming Agile: How the SEAM Approach to Management Builds Adaptability[END_REF] is inscribed in the inter-actionist trend which considers that organizations are the result of interactions between individuals [START_REF] Blumer | Sociological implications of the thought of George Herbert Mead[END_REF]Berger and Luckman, 1966). Logically the fundamental theoretical hypothesis of the socio-economic approach can be close to the Complex Thought: in any organization there are permanent interactions between structures (demographic, mental, etc.) and behaviours (individual, group, etc.).These interacting structures and behaviours produce emergences, in our case dysfunctions causing costs that thwart the performance of the enterprise and are an obstacle to the auto-econ-re-organization.

A strength of the socio-economic management is to invite managers to couple Cartesianism and complexity and not to oppose them. In this perspective, the socio-economic management offers a work method to operationalize the Complex Thought along three inter-dependent axes conditioning the survival and development of establishments in an uncertain environment: the axis of the process of change, the axis of the socio-economic tools and the axis of political decisions. These three axes permit to deploy a management linking strategy and operational actions according to the dialogic, hologrammatic and recursive principles guaranteeing the auto-eco-re-organization.

4.2

The three axes of the socio-economic management to manage the auto-ecore-organization The 'process of change' axis enables the actors of the establishment to evidence the dysfunctions in different domains (working conditions, work organization, communication, etc.). Once the causes of these dysfunctions are identified, change actions should be put in place to mitigate them. The process also measures the financial impacts of the actions implemented by evaluating the reduction of hidden costs and increase in performance. This axis then offers the actors the opportunity to define and implement a project permitting to fight, as in the case studied, against the lack of equipment, the compartmentalization of teams or the training plans without effects.

The 'tools' axis naturally offers tools for the concrete implementation of change actions. The socio-economic tools are also indicators of alert when the dysfunctions appear. They support the process of change by permitting to be vigilant about the emergences.

-

The activity contract regularly negotiable formalizes the objectives and the means available for attaining them.

-

The competencies grid permits to visualize the polyvalence and vulnerabilities of competencies inside a team. Thus, the elaboration and implementation of training plans can be adapted to the needs of the establishment.

-

The internal-external strategic action plan formalizes the internal strategy for all the actors of the organization, as well as the external strategy for the stakeholders outside the organization. The plan of priority actions then states the actions to be implemented over one semester inside each service.

-

The monitoring dashboard groups the indicators necessary for the monitoring of activities. It is essentially used by the management to control and evaluate in qualitative, quantitative and financial terms the implementation of the strategic and organizational actions.

-

The time self-analysis grid lists the tasks performed over a set period with the aim of structuring the timetables in the most effective way.

The 'political decisions' axis directly and indirectly influences the various domains of the functioning of the organization. The political decisions contribute to ensuring the survival and development of the organization, that is its auto-eco-re-organization.

On the one hand the socio-economic management nurtures a complex vision of the organization by tackling the root causes of the dysfunctions and making observable data concerning them (e.g. hidden costs). On the other hand the socio-economic management offers the possibility to implement a process of change, develop policies and implant tools to monitor the dialogic, hologrammatic and recursive principles. This monitoring is indispensable for the survival and development of the establishment.

Conclusion

The question dealt with in this article is that of the role that the Complex Thought, as defined by Edgar Morin, can play in the monitoring of health organizations. The hypothesis tested suggests that the lack of understanding of the Complex thought directly impacts the social and economic performance of the establishments. The results of the research carried out in a Home for Dependent Elderly Persons validate this hypothesis. They reveal that the organization generates costly dysfunctions and emergences, in Morin's sense, which are obstacles to the auto-eco-re-organization and then challenge the survival and development of the establishment in an uncertain environment.

This unique case study permits to confirm, test and enrich Morin's theory [START_REF] Yin | Case Study Research; Design and Methods[END_REF] by evidencing the cost of ignoring the Complex Thought in the context of a group of medical and social group. These results, however, only allow a theoretical generalization and will have to be supported by others in other establishments.

These results lead to the following proposition: the epistemological conditions of the establishments do not favour a monitoring according to the Complex thought. The latter could, nevertheless, become operational thanks to the engineering of the socio-economic management permitting to pilot the auto-eco-re-organization of establishments.


Paul Eyméoud
email: paul.eymeoud@im2np.fr

Dmytro Kandaskalov

Philippe Maugis

Impact of stresses and alloying elements on ferrous martensite nanodomains

Keywords:

Using first-principles calculations, we investigated the impact of applied stresses and alloying elements on ferrous martensite nanodomains. In non-alloyed martensite, the procedure revealed that twinned states can be stabilized depending on applied stresses, leading to several possible crystallographic structures: body-centered tetragonal (BCT) oblate, body-centered orthorhombic (BCO), or BCT prolate. In alloyed martensite, we confirmed the experimental data from literature showing that Al or high Ni addition disfavors crystal twin formation (leading to BCT variants with high tetragonality ratios), whereas Cr, Mn, or Re addition favors crystal twin formation (leading to BCO variants with low tetragonality ratios).

Introduction

The crystal structure of freshly quenched ferrous martensite appears quite controversial in the literature.

In the case of non-alloyed martensite, a majority of experimental investigations [1,2,3,4,5,6,7] detected a body centered tetragonal (BCT) prolate host lattice occupied by iron atoms, with carbon atoms located in octahedral interstitial sites (o.i.s.). Concerning the distribution of C atoms in these o.i.s., several mean-field models [8,9], based on elasticity theory, conclude to the stability of the so-called Zener ordering 𝛼 ′ , namely preferential distribution of C on one among the three o.i.s. Such particular ordering has been later confirmed by first-principles calculations [10] based on the Special Quasirandom Structures (SQS) technique [11].

The tetragonality ratio c/a of those non-alloyed BCT martensites has been fitted as a linear function of C content by several authors [7]. In this work, we will refer to Kurdjumov's fit [12], where 𝑝 denotes mass percent of C:

𝑐∕𝑎 = 1 + 0.046𝑝 (1)
However, both BCT prolate structure and equation ( 1) have been challenged by several sources.

First, in the simplest case of non-alloyed martensite, orthorhombic crystals with anomalously low 𝑐∕𝑎 𝑚 (with 𝑎 𝑚 = (𝑎 + 𝑏)∕2) with respect to eq. ( 1) were detected by Lysak [13]. On top of that, calculations of Ruban et al. [14,15], based on both first-principles and Embedded-Atom Method calculations, demonstrate the stronger thermodynamical stability of particular BCT oblate structures, with respect to Zener ordering.

Second, in the more complex case of alloyed martensite, two specific kinds of crystalline anomalies have been detected.

The first kind of crystalline anomaly, called "𝜅 ′ martensite", is exactly similar to the one detected by Lysak in nonalloyed martensite [13]. It corresponds to an orthorhombic lattice with abnormally low 𝑐∕𝑎 𝑚 with respect to eq. ( 1), and has been detected in martensite alloyed with Cr [2], Mn [16], Re [17], and low Ni content [18].

The second kind of crystalline anomaly corresponds to a BCT prolate lattice with abnormally high c/a with respect to eq. ( 1), and has been detected in martensite alloyed with Al [19,20,21] and high Ni content [22,23,24].

Among the numerous investigations attempted to explain those anomalous tetragonalities [12,24,19,25], starting from X-ray results [26] Kurdjumov and Khachaturyan [2,12] demonstrated that a nano-twinning mechanism can explain the case of anomalously low tetragonalities with orthorhombicities. Following this hypothesis, we propose a first-principles investigation involving nano-twinned structures, in order to provide additional information to shed light on the link existing between martensite crystallographic changes and alloying elements.

This work is decomposed as follows. After briefly presenting our first-principles modelling techniques, we first focus on the case of non-alloyed martensite, by studying the comparative energetic stability of twinned and non-twinned configurations under several applied stresses, and associated crystalline structure. In a second part, we introduce the effect of alloying elements on host lattice, and evaluate their impact on twinning and crystalline changes.

Computational techniques

First-principles calculations have been performed using VASP code [27,28] (in-house version allowing to impose stresses on cells [10]), with generalized gradient approximation [29], projector augmented wave method [30] and Perdew-Burke-Ernzerhof exchange-correlation functionals [31,32], spin-polarized approximation, 400 eV energy cutoff, 10 -5 eV (resp. 10 -4 eV) for electronic self-consistency (resp. ionic relaxation criterion).

Calculations related to non-alloyed martensite (at 12. Color code: grey (resp. blue) for Fe (resp. alloying element), red (resp. green) for C located in X-type (resp. Y-type) o.i.s., dashed purple for twin interfaces. For each supercell, the coordinates file is given as supplemental material.

[33]). Concerning the carbon distribution on those o.i.s., we assumed the 𝛼" distribution [34] (I4/mmm) as a rough approximation of Zener ordering 𝛼'. Such 𝛼" distribution, corresponding to a particular case of Zener ordering 𝛼', has been determined as the lowest energy distribution by DFT calculations [35], and suggested to form during spinodal decomposition using atom probe tomography [36]. What is more, choosing this 𝛼" distribution allows to avoid the timeconsuming calculations on several sets of SQS necessary to represent the usual 𝛼' [10].

The nanodomains we considered are nanotwins with various proportions but same wavelength. Five different carbon distributions were studied (see Fig. In order to treat the case of alloyed martensite, we have approximated the 25at%M alloying case for M=Al, Ni, Cr, Mn, Re, using two different M-Fe ordered distributions on the host lattice (Fig. 1, right): (i) a BCT ordered repartition corresponding to L1 2 perovskite after Bain transformation (see Ref. [37,19]), (ii) a DO 3 ordered repartition.

Results for non-alloyed martensite

We have computed the formation enthalpy of each of the five non-alloyed configurations of Fig. 1 left , taking for reference the non-twinned distribution with 100% of C in X-type o.i.s., using the following equation:

Δ𝐻 = Δ𝑈 -𝑉 𝝈 ⋅ Δ𝜺
wherein 𝑈 denotes the internal energy, 𝑉 the volume of the stress-free carbon-free crystal, 𝝈 (resp. 𝜺) the stress (resp. strain) tensor.

We imposed a shear stress on our structures, with several amplitudes (0GPa < 𝜎 𝑌 𝑌 = -𝜎 𝑋𝑋 < 0.5GPa), and also a pure tension 𝜎 𝑌 𝑌 = 1.0GPa and a pure compression 𝜎 𝑌 𝑌 = -1.0GPa along (Oy). Those results, presented on Fig. 2, allow us to draw the following conclusions.

Under weak shear stress (amplitude lower than 0.075GPa), twinning stabilizes the structure. In this case, the most stable variant is the "50% of C in X-type o.i.s.", with BCT oblate crystalline structure. Such result agrees with Ruban's calculations [14,15], stabilizing a BCT oblate structure.

Under "moderate" shear stress (amplitude between 0.075GPa and 0.225GPa), the minimum of enthalpy corresponds to the "25% of C in X-type o.i.s." twinned variant, whose crystal structure is orthorhombic with low 𝑐∕𝑎 𝑚 , in coherence with measurements from [13].

Finally, under "strong" shear stress (amplitude higher than 0.225GPa), the non-twinned variant "0% of C in X-type o.i.s." is the most stable structure, which is consistent with the aforementioned sources [1, 2, 3, 4, 5, 6, 7] claiming the stability of BCT prolate martensite, with Zener ordering.

Moreover, being conscious that, in steels, freshly formed martensite undergoes several kinds of external stresses, our computational results from Fig. 2 left can partially explain why experimentalists generally observe, without alloying elements, BCT prolate with Zener ordering, or orthorhombic with low 𝑐∕𝑎 𝑚 martensite, rather than BCT oblate martensite, which is yet numerically stabilized as particular/twinned superlattices.

Such changes of stabilities induced by shear stress are linked to the fact that tensile (resp. compressive) stress favors full Zener ordering along traction (resp. orthogonal to compression) direction, which can be seen on Fig. 2, right, in coherence with Ref. [10,38]. On top of that, one can notice the graphical superposition between shearing 𝜎 𝑌 𝑌 = -𝜎 𝑋𝑋 = 0.5GPa and pure tension 𝜎 𝑌 𝑌 = 1GPa (resp. shearing 𝜎 𝑌 𝑌 = -𝜎 𝑋𝑋 = -0.5GPa and pure compression 𝜎 𝑌 𝑌 = -1GPa), enhancing the preponderance of 𝜎 𝑌 𝑌 -𝜎 𝑋𝑋 deviatoric part of stress tensor.

Although the previous results are based on a specific carbon distribution in o.i.s. (𝛼"), its validity can be generalized, since the 𝛼" distribution is a particular case (lowestenergy distribution [35]) of the more general 𝛼' one. By replacing the set of 𝛼" twinned and non-twinned ordered variants of Fig. 1 by several sets of 𝛼' twinned and nontwinned disordered SQS [10], one can reach, after averaging, the same stability results presented on Fig. 2, provided that the number of SQS is sufficient.

Results for alloyed martensite

We have computed, at zero stress, the formation enthalpy of each configuration of Fig. 1, in the alloyed case. For that, we have changed the iron host lattice by a Fe-M host lattice at 25at%M, using two kinds of approximations to represent alloying (cf. Section 2).

The results, presented on Fig. 3, left, allow us to split the alloying elements in two categories, depending on formation enthalpy sign: Mn, Cr, or Re addition energetically favors twinning, whereas Al or Ni addition energetically disfavors twinning (strongly for Al, and slightly for Ni). An important point is the fact that both ordered host lattices (L12+Bain and DO3) lead to the same dichotomy (Al, Ni on the one side, and Cr, Mn, Re on the other side), despite their strong symmetry difference (in carbon-free case, L12+Bain is BCT, and DO3, BCC). Therefore, we can assume that the classification "Al, Ni versus Cr, Mn, Re" does not depend on host lattice symmetry or ordering, and is thus valid for any other alloying element distribution on host lattice.

Moreover, if one applies a shear stress on those alloyed martensite structures, two situations can occur depending on the alloying element employed: (i) for Mn-, Cr-or Realloyed martensite, the crystallographic behavior is the same than non-alloyed martensite (cf. Fig. 3, center), namely BCT oblate structure under weak stress, orthorhombic with low 𝑐∕𝑎 𝑚 under moderate stress, and BCT prolate under strong stress, (ii) for Al-and Ni-alloyed martensite, the most stable structure remains the BCT prolate one without twins, whatever the amplitude of imposed shear stress (cf. Fig. 3, right).

Such dichotomy (non-alloyed, Mn, Cr, Re versus Al and Ni) matches very well the experimental observations from literature. On the one hand, the orthorhombic lattice with low 𝑐∕𝑎 𝑚 detected in non-alloyed, Mn-, Cr-and Re-alloyed martensite results from presence of twins. On the other hand, the BCT prolate lattice detected in Al-and high-Ni-alloyed crystals is caused by the absence of twins, and the associated abnormally high c/a results from the host lattice softening induced by alloying elements [35]. Moreover, in the specific case of Ni, the slight tendency to disfavor twinning appearing on Fig. 3 left coincides with the ambivalent observations on Ni-alloyed martensite depending on Ni concentration: tendency to form orthorhombic structures with low 𝑐∕𝑎 𝑚 at low at%Ni [18] (situation close to the non-alloyed red plot on Fig. 3 left), versus tendency to form BCT prolate structures with high c/a at high at%Ni [22,23,24] (situation close to the 25at%Ni-alloyed orange plots on Fig. 3 left).

Conclusion

Using first-principles calculations, we have compared the thermodynamic stabilities of twinned martensite structures with respect to non-twinned ones.

In the non-alloyed case, we have managed to reconciliate the controversial data from literature concerning non-alloyed martensite crystalline changes. Because of twinning, the theoretical most stable structure at zero stress appears to be BCT oblate, in coherence with Ruban's calculations [14,15]. However, since freshly formed martensite undergoes several kinds of stresses, experimentalists almost always observe BCT prolate structures with Zener ordering [1,2,3,4,5,6,7], that are most stable under strong applied stresses which disfavor twinning. Nethertheless, in some cases where the applied stresses are moderate, some twinned orthorhombic structures with low 𝑐∕𝑎 𝑚 can be detected [13].

In the alloyed case, we explained the two kinds of crystalline anomalies found in literature [12] and confirm their twinning origin. On the one side, Mn-, Cr-, and Realloying favors twinning, leading, under applied stresses, to orthorhombic structures with low 𝑐∕𝑎 𝑚 ratios. On the other side, Ni-and Al-alloying disfavors twinning whatever the applied stress, leading to BCT prolate structures with high c/a ratios.

  5at%C) were performed on 8 × 8 × 2 BCT supercells containing 256 Fe atoms, and 32 C atoms located in o.i.s. (associated kpoints representation: 2 × 2 × 8 Monkhorst-Pack scheme

Figure 1 :

 1 Figure1: Supercells used for calculations: interstitial C twinning from 0% to 100% of X-type (left), two approximations of alloying on host sublattice, transformation of L1 2 and DO 3 (right). Color code: grey (resp. blue) for Fe (resp. alloying element), red (resp. green) for C located in X-type (resp. Y-type) o.i.s., dashed purple for twin interfaces. For each supercell, the coordinates file is given as supplemental material.

  1, left): (i) two nontwinned distributions, namely 𝛼" ordering in X-type o.i.s. and 𝛼" ordering in Y-type o.i.s., (ii) three (110) twinned distributions, corresponding to 25% (resp. 75%) of C in Xtype (resp. Y-type) o.i.s., 50% (resp. 50%) of C in X-type (resp. Y-type) o.i.s., and 75% (resp. 25%) of C in X-type (resp. Y-type) o.i.s.

Figure 2 :

 2 Figure 2: Crystal twin formation enthalpy in non-alloyed martensite (reference: 0%X variant taken under same stress). Left: under stress (color code denotes, for each plot, the minimum enthalpy: red for BCT oblate 50%X variant, blue for orthorhombic 25%X variant, and green for BCT prolate 0%X variant). Right: under shear, tensile and compressive stress.

Figure 3 :

 3 Figure 3: Crystal twin formation enthalpy for alloyed martensite (reference: 0%X variant taken under same stress). Left: under zero stress. Center (resp. right): case of Mn-alloyed (resp. Al-alloyed) martensite, under imposed shear stress.

Acknowledgments, Data availability statement

This work was supported by the Agence Nationale de la Recherche (contract C-TRAM ANR-18-CE92-0021). Centre de Calcul Intensif d'Aix-Marseille is acknowledged for granting access to its high performance computing resources. Paul Eyméoud thanks Armen Khachaturyan for fruitful discussions, and Damien Connétable for sharing his VASP in-house version allowing to impose stresses on supercells.

Data are available upon request.

CRediT authorship contribution statement

Paul Eyméoud: Conceptualization, Methodology, Software, Writing -Original Draft, Writing -Review and Editing. Dmytro Kandaskalov: Methodology. Philippe Maugis: Supervision.