tyaglova. Svetlana Tyaglova-Fayer
email: fayer.svetlana@sfr.fr

New technology to understand the secrets of Saharan beliefs through the tattoos of the very first tattooed people

Keywords: The first tattooists, the civilization of the Great Goddess, the Snake Goddess, the collapse

. Apparently, all the bodies had been buried in the foetal position, at a shallow depth in the sand, in accordance with predynastic traditions and surrounded by objects echoing Saharan rock art. The first approach which permits understanding these traditions shows that, until now, researchers have focused on highlighting a possible community of forms between Saharan rock art and Egyptian art, or a common mythological content that would have been conveyed by these two art forms (D'Huy & Le Quellec, 2009: 85). This quest for origins seems to ignore the violence and brutal changes associated with the process of state formation in Egypt, as well as the break with certain traditions that may have resulted. Recently, thanks to new technologies, scientists have discovered trauma 1 and tattoos 2 on two of Gebelein's bodies (horned beasts on the man's arm, four 'S' symbols on the woman's upper shoulder and an 'L' on her arm). The date of death of these two individuals has been estimated at between 3,351 and 3,017 BC. It should be noted that it was not until the Ramses' period 3 that tattoos were found on a mummified body (Blakemore, 2023). We believe that profound societal and religious changes were at the root of this abrupt rupture, which lasted for almost two thousand years.

Une nouvelle technologie pour comprendre les secrets des croyances sahariennes à travers les tatouages des tous premiers tatoués

Résumé: Plusieurs corps humains naturellement momifiés ont été exhumés près de Gebelein (40 km au sud de Thèbes). Six d'entre eux (EA 32751-32756) ont été obtenus pour le musée britannique (British Museum) en 1899 par Sir E. A. Wallis Budge, qui a affirmé avoir assisté à leur fouille [START_REF] Budge | By Nile and Tigris: a Narrative of Journeys in Egypt and Mesopotamia on Behalf of the British Museum between the Years 1886 and 1913[END_REF]. Apparemment, tous les corps avaient été enterrés en position foetale, à une faible profondeur dans le sable, conformément aux traditions prédynastiques et entourés d'objets faisant écho à l'art rupestre saharien. La première approche pour comprendre ces traditions montre que, jusqu'à présent, les chercheurs se sont plutôt attachés à mettre en évidence une éventuelle communauté de formes entre l'art rupestre saharien et l'art égyptien, ou un contenu mythologique commun qui aurait été véhiculé par ces deux formes d'art (D'Huy & Le Quellec, 2009 : 85). Cette quête des origines semble ignorer la violence et les changements brutaux liés au processus de formation de l'État en Égypte, ainsi que la rupture avec certaines traditions qui a pu en résulter. Récemment, grâce à de nouvelles technologies, les scientifiques ont découvert des traumatismes et des tatouages sur deux corps de Gebelein (les bêtes à cornes sur le bras de l'homme, quatre symboles "S" sur le haut de l'épaule de la femme et un "L" sur son bras). La date de la mort de ces deux individus a été estimée entre 3 351 et 3 017 BC. A noter qu'il faut attendre l'époque ramesside pour retrouver des tatouages sur un corps momifié [START_REF] Blakemore | Le mystère des momies tatouées[END_REF]. Nous pensons que de profonds changements sociétaux et religieux sont à l'origine de cette rupture brutale, qui a duré près de deux mille ans.

Mots-clés:

Les premiers tatoués, la civilisation de la Grande Déesse, la Déesse Serpent, l'effondrement de l'âge de bronze, rupture bimillénaire dans la pratique du tatouage.

Introduction; method and hypothesis

In FLE (teaching French as a foreign language), it is common to draw parallels with the mother tongue. We applied our linguistic methods to archaeological analysis. Our method of comparison by parallels was born. It makes it possible to 'read' archaeological artifacts in their overall context by following the evolution of their concepts in space-time. In this article, we put forward the hypothesis that the 'S' and 'L' found on the woman's body represent the snake: a symbol of divine power that would later be found not only in dynastic Egypt, but also much further north.

In our opinion, this could be a cultural code whose iconography reflects ancestral beliefs, in which the feminine was associated with the snake and the masculine with the horned beast. According to the theory of Marija Gimbutas [START_REF] Gimbutas | The Gods and Goddesses of Old Europe, 7000 to 3500 BC. : Myths, Legends and Cult Images[END_REF][START_REF] Gimbutas | La fin de l'Europe ancienne[END_REF][START_REF] Gimbutas | Le Langage de la Déesse (trad. Jean Guilaine)[END_REF] these beliefs, common to a very large area (referred to here as the 'common cultural horizon'), have persisted over a long period. We hope that new technologies (digitization of archives, infrared imaging, scanners, etc.) and the parallels that can be drawn between the Nagada culture4 and similar cultures in space-time will help us to understand the origin of the break in the practice of tattooing and the beliefs associated with it among the peoples of the Predynastic period.

We were struck by the hypothesis of two American archaeologists (Dennis J. Stanford and Bruce A. Bradley)5 who sought to explain how it is possible to observe similarities between cultures that are distant in time and space. For example: the Solutrean culture (Upper Paleolithic in Europe) has similarities with the culture found at an archaeological site in the state of New Mexico (near the town of Clovis) in the United States. Hundreds of thousands of miles and more than 10,000 years separate these two cultures! Our hypothesis of a "common cultural horizon" may go some way to explaining this phenomenon. We know that sapiens left Africa between 190,0006 and 30,000 years ago, in several waves of migration. It is assumed that these sapiens had beliefs that made them more confident than other hominids. Armed with these beliefs and the cultures and new technologies they developed; they dominated other populations (notably the Neanderthals)7 . Their 'Venus's figurines' can be found wherever they went, migrating across Europe, Asia, Siberia and America.

The content

The application of tattoos to the human body has a history in many ancient cultures. Until now, the earliest examples were mainly geometric tattoos of the individual known as Ötzi -the Iceman [START_REF] Deter-Wolf | The world's oldest tattoos[END_REF], dating from the late 4th millennium BC. (3370-3100 BC.), whose skin was preserved by ice. He had 61 tattoos of lines and crosses all over his body. Given that they were mainly grouped on the parts of his body where he would have felt discomfort due to the degenerative diseases from which he suffered (around his lower back and joints), we can deduce that the application of these tattoos had a medical rather than a symbolic purpose.

Unlike Ötzi's tattoos, the tattoos on our two Predynastic Gebelein mummies appear to be highly symbolic in nature, since they are applied to parts of the body (arm and shoulder) exposed to the gaze of others, and their iconography comes from the rock art of the time. It is currently accepted that these are the oldest figurative tattoos known [START_REF] Friedman | Natural mummies from Predynastic Egypt reveal the world's earliest figural tattoos[END_REF].

The fact that there was a break in this almost two-thousand-year-old practice intrigues us and is the subject of our reflections. Indeed, it was not until the Ramses' period that tattoos were found on a mummified body [START_REF] Blakemore | Le mystère des momies tatouées[END_REF] 8 . We believe that profound societal and religious changes were at the root of this abrupt rupture. We're going to delve into the archaeological archives to understand this break with the past.

The first approach shows that "until now, researchers have tried to highlight a possible community of forms between Saharan rock art and Egyptian art, or a common mythological content that would have been conveyed by these two art forms" (D'Huy, J. & Le Quellec, 2009: 85). This quest for origins seems to ignore the violence and brutal changes associated with the process of state formation in Egypt during the installation of the first dynasties, as well as the break with certain traditions that may have resulted. Let's take a look at each of the tattoo motifs on our mummies.

1) The image of horned animals:

According to some archaeologists, the horned animals found on Gebelein Man are frequent features of ancient Egyptian iconography, but identifying the intended species remains a challenge [START_REF] Friedman | Natural mummies from Predynastic Egypt reveal the world's earliest figural tattoos[END_REF]. Based on the shape of its elaborate horns and long tail, the lower tattoo represents an ox (most likely a wild bull) and the upper tattoo suggests it is a Barbary sheep (idem).

Incidentally, this tattooed man has shattered a legend according to which only women were tattooed for reasons of fertility or even eroticism (idem).

According to studies by Julien d'Huy and Jean-Loïc Le Quelle, in the eyes of the Egyptians, each image was a living being endowed with its own magical power and effectiveness (D'Huy, J. & Le Quellec, 2009: 93).

Given that the wild bull was one of the three heraldic figures of Predynastic Egypt, along with the falcon and the lion [START_REF] Graff | Image, écriture et communication en Égypte pré-pharaonique, Les Tables Rondes de l'Arbois[END_REF], we can deduce that this tattooed man was part of an emerging elite in the culture of Nagada II -III.

Given his violent death 9 , and the sudden break with certain traditions such as the disappearance of tattoos for two thousand years, the change in the posture of the body of the deceased (the foetal position was replaced by the position on the back in dynastic Egypt), and the shape and content of tombs (a radical change in funerary furnishings, to which we will return later), we can legitimately assume that this elite was eliminated or, rather, migrated (since we note the return of the practice of tattooing thereafter).

2) The image of the stick (« L »)

Like the previous motif, the 'stick' is a fairly common element in Saharan rock art. It is often used as a magical object to control wild animals, particularly in hunting scenes. From the period commonly known as the "Round Heads" (8000±900 BC), dated by Jean-Loïc Le Quellec (Le Quellec, 2013), to the "Iheren" style (around 3000 BC), these sticks are held by women. Later, the 'sticks' were replaced by bows and lassos: see Figures 1-3 by Lankester [START_REF] Lankester | L'art rupestre et les rites de passage des élites naissantes au Prédynastique égyptien, Archéologie et art de la vallée du Nil à l'Holocène moyen[END_REF]. The gender of the people holding these objects no longer has any obvious female characteristics.

3) The image of the « S »

Unlike the previous motifs, this one is completely new. Without being able to rely on the archives, we're taking the liberty of applying our method of parallels to understand its symbolism.

In our opinion, the 'S' on the tattooed woman's shoulder refer to the snake in their graphic form. This point of view is confirmed by the Egyptian hieroglyphs (N°13193, 13197 and 13193) 10

Let's take a look at the cultural horizon of this symbol across space and time: -It is found in abundance at Göbekli Tepe in sculptural and graphic versions (Schmit, 2015;[START_REF] Шмит | Они строили первые храмы. Таинственное святилище охотников каменного века : археологические открытия в Гёбекли Тепе[END_REF] and in the rock art of the Sahara Desert [START_REF] Mostefai | Les représentations féminines d'Ozan Ehéré (Tasīli-n-Ajjer, Sahara central, Algérie[END_REF];

1)
2)

3)

The evolution of the concept of divine power represented by the snake in chronological order: Images 1 and 2, sculpture and engraving from Göbekli Tepe (c. 6000 BC): a stone head with a snake on its skull and a woman giving birth with a snake's head (Photos courtesy of Vincent J. Musi). Image 3, The Libyan Messak engraving (c. 4000 BC, photo courtesy of Van Albada, 1996:10) -This symbol very often adorns and is even an essential element of the headdresses of the Egyptian pharaohs and their gods (Guillou & Pevré, 2014); it is usually in an "L" shape, but sometimes in a "U": -It travelled thousands of years and miles to appear among the Minoans (see the statuettes from Knossos; [START_REF] Evans | The prehistoric tombs of Knossos[END_REF].

6) 7)

Images 6 and 7, Statuettes from Knossos (photos mythagora.com) dated around 1600 BC.

These last two images associated with the snake can help us to understand the evolution of this concept, which is apparently migrating northwards through time and space. This series of feminine images echoes the prehistoric 'Venuses'. As far as these prehistoric 'Venuses' are concerned, it is worth noting that a famous archaeologist, Marija Gimbutas [START_REF] Gimbutas | Civilization of the Goddess: The World of Old Europe[END_REF], carried out archaeological digs (over several decades), accumulating traces of funerary rituals in which these representations (statuettes and female figures painted on ceramics) were too frequent not to be noticed. It was then that Marija Gimbutas put forward a new hypothesis. What if these female figures represented a Great Goddess?

If we compare pre-dynastic Saharan funerary traditions, we find many similarities in the funerary rituals of the same period noted by Mrs Gimbutas over a vast territory (cultural horizon) stretching from the Middle East to Eastern Europe.

To illustrate this, let's compare the funerary practices of the RUBANEA Culture (Гимбутас, 2006) and those of the Nagada Culture (Graff, 2008: 169-182).

Here, we note that the RUBANEA is the oldest Neolithic culture in Europe. It dates from 5500-4700 BC and spread to northern France and Belgium (the Entre-Geer-et-Meuse region), western Germany, Hungary, the Czech Republic, Moldavia, Romania and Ukraine. It is characterized by a high degree of uniformity in its material culture. The rituals of cremation are to be found here, but burial was much more common. Burials are almost all individual and shallow. The bodies lie in the foetal position, most often on their left side, with their hands in front of their faces, their heads facing east and their eyes facing south (Гимбутас, 2006: 87-89).

As for the Nagada culture, its 750-year history is clearly stratified. This is why archaeologists divide it into three periods. During the first period (Nagada I), the burials were almost all individual and uniform. At the end of Nagada II and throughout the Nagada III period, the hierarchy -a sign of social inequality -was so obvious that different spaces appeared in the necropolises: on the one hand, large, richly furnished tombs for the elite and, on the other, much more modest burials (sometimes even communal). However, there is one constant: all the bodies are folded on their left side, with their hands in front of their faces (Graff, 2008: 170), which is a common feature of the RUBANEA Culture. On the other hand, the head of the Saharan deceased is oriented towards the south and his eyes towards the west (idem). We believe that the eyes facing west (towards the setting sun) prefigure future beliefs, in which this orientation will represent the world of the dead west of the Nile and the world of the living east of it (the Nile will be the boundary between these two worlds).

Let's take a look at the funerary objects that accompany the deceased in both cultures. There's another similarity: funerary vases. Even if the construction and shapes of these funerary vessels differ in the two cultures, their presence in tombs is an indisputable constant. In the Nagada culture, even the poorest tombs contained one or two of these vessels (Graff, 2008: 173). These similarities allow us to extend the common cultural horizon beyond the fixed borders of the Levant to Nubia (Graff, 2008: 180) and to propose the following series of images to our reader: While images 1 to 10 show that the snake symbol is more specifically feminine (although horns do appear and become confused with snakes in later periods), this series focuses on man, who presents himself as 'master of the animals' (except image 14). We can therefore see that the concept of 'master of the animals' in the 'masculine' appears in the Neolithic, reflecting the process of domestication of wild animals and the establishment of a new societal order, even if certain territories (mainly located on islands) still resist (see also image N°14).

In fact, at the dawn of the Neolithic (Mesolithic) period, Palaeolithic beliefs linked to the cult of the Great Goddess, still visible at Göbekli Tepe (images 1 and 2) and in Libya (image 3), began to change following the transformation of hunter-gatherers into the first 'farmers' with the emergence of livestock rearing and agriculture in the 'Fertile Crescent'. Indeed, at the time, Mesopotamia, with its pleasant climate and abundant natural water resources, was the ideal place for the birth of agriculture.

A little later, Neolithization also took place in the Sahara, only in the regions around the Nile. In fact, consecutive arid phases forced the Saharan peoples to regroup around the Nile, as the large fauna of the Sahara began to disappear and hunting was no longer sufficient for their survival. As early as Nagada I, the consumption of meat from hunting had fallen from 10% in the Badarian period (the culture preceding Nagada) to just 1% around 3800 BC (Lankester, 2016: 88). However, hunting retained a symbolic character, remaining practiced by the emerging elite and forming part of their rituals associated with initiation and the justification of a privileged status (idem).

New activities (animal husbandry and agriculture) replaced hunting in Nagada from the outset. This led to social stratification, creating a hierarchical pyramid in which the most productive farmers were the best placed. This social stratification was no longer compatible with the beliefs associated with the Great Goddess. It should be noted that the funerary inventory specific to these beliefs shows that the worshipers of the Great Goddess lived in rather egalitarian societies [START_REF] Gimbutas | Le Langage de la Déesse (trad. Jean Guilaine)[END_REF].

Whereas in the Paleolithic, hunter-gatherers took what the land and nature gave them, remaining totally dependent on their generosity, in the Neolithic, the land lost its sacred character and became a source of covetousness for humans: it was the strongest who won the right to cultivate its best plots. Beliefs changed, as did funeral rituals.

There was a change in the posture of the deceased: the foetal position was replaced by the supine position in dynastic Egypt. The ancient beliefs of hunter-gatherers linked to the veneration of the Great Goddess were therefore replaced by beliefs linked to new activities (livestock rearing and agriculture), but clay statuettes (echoing prehistoric "Venuses") were still found in tombs until the beginning of Nagada III (Graff, 2008: 174).

We believe that the foetal position is linked to the belief in reincarnation in the 'womb' of the Great Goddess Mother Earth, while the supine position is probably linked to the new beliefs in resurrection.

To return to our tattooed mummies, we assume that they were among the last worshipers of the Great Goddess, condemned to die or migrate in the face of the new societal order emerging in dynastic Egypt.

Indeed, their violent deaths (cranial trauma in the case of the woman and a stab wound in the back in the case of the man), their foetal position, the lack of funerary objects (a person who believes he is being reincarnated in a new body does not need as many objects as someone who intends to be resuscitated) and the absence of defensive lesions suggest that they were the last worshipers of the Great Goddess.

In cave art, the evolution of motifs is a source of food for thought. In the Paleolithic, cave art was invisible. Lurking deep in uninhabited caves, to contemplate it you often had to travel hundreds of feet underground, bringing your own source of light with you. This is in line with the concept of the "sacred womb of Mother Earth" that can still be seen at Nagada I : Around the Neolithic period, rock art became observable in daylight. In contrast to the previous period, the subjects become very varied. There are all kinds of animals, humans, more or less human figures with their arms raised, often large ones, weapons, chariots, dwellings, trees and so on. These figures are usually organized into scenes: pastoral, hunters and warriors are the most common themes [START_REF] Anati | Aux origines de l'art, 50 000 ans d'art préhistorique et tribal[END_REF]. Curiously, the only theme that remains common to Palaeolithic and Neolithic art is that of negative hands. Can this be explained by the importance attached to hand production throughout the ages? We have no answer to this question. Whatever the case, these new beliefs clearly gave rise to a whole "afterlife industry" not only in Predynastic Egypt (from the end of Nagada II) but also in other regions of the Mediterranean.

As Gwenola Graff notes, some of the objects deposited in the tombs (related to wine and oil, as well as palettes and club heads, whose choice of material or abundance of decoration make them "unusable"), especially from the end of the reign of Nagada II, were intended to underline the symbolism of a certain social status, and were very often brought from other regions of the Mediterranean (Graff, 2008: 179-180).

Coming back to our tattooed mummies (which unfortunately have no funerary objects), based on our previous analysis (paragraphs N°1-3) we can legitimately assume that their tattoos12 were markers of a certain social status of the elite who had not found their place in dynastic Egypt. The two-thousand-year break in the practice of tattooing suggests that this elite must have migrated, only to return later.

Analysis of archives and images gives plausibility to our hypothesis: the tattoos found on the skin of our mummies are highly symbolic and probably refer to a divine power where the 'masculine' is associated with the magical power of horned beasts (paragraph 1) and the 'feminine' with that of the snake (paragraphs 2-3). We also note that the cultural horizon of the great goddess Mother Earth broke down during the Neolithic period, gradually replacing the 'feminine' (images N°1 to 10) with the 'masculine' (images N°11 to 13). The break was a violent one, and our mummies bear the marks of it (see notes 1 and 9).

Conclusions and future research

At the dawn of the Neolithic (Mesolithic), Palaeolithic beliefs linked to the cult of the Mother Goddess, still visible in Turkey (Göbekli Tepe) and Libya (Messak), began to change. This change spread beyond the Fertile Crescent, prompting populations wishing to preserve their ancient beliefs to migrate northwards (images 6 to 10). A new social order (patriarchy) was established. Under this order, the land lost its sacred character and became an object of covetousness, provoking wars and violence. Some of the population continued to resist, taking refuge on islands (photo 14). Others (like our mummies) fell victim to this brutal change in civilization. When the Bronze Age collapsed, there were no longer any followers of the ancient beliefs on the shores of the Mediterranean: funeral rites (position of the deceased, objects accompanying him/her, etc.) changed. We assume that the worshipers of the Great Goddess survived in spite of everything, moving towards the north-east (see images 9 and 10), but this hypothesis will be the subject of further study. In this next article, we will also look at the myths relating the killing of the serpent or dragon in various popular legends which, in our view, illustrate the transition from feminine to masculine monotheism. Here's an overview in pictures:

10.

  Les numéros indiqués font partie de " Unicode standard" https://symbl.cc/ru/unicode/blocks/egyptian-hieroglyphs/ The goddess Hathor welcomes SETI I (1294 to 1279 BC; Paris, Musée du Louvre; https://www. photo.rmn.fr); Image 5, Emblem of the goddess Hathor (Paris, Musée du Louvre; https://www.photo.rmn.fr), N.B, it is not clear whether she has a snake or horns on her head.

  Minoan pendant "Mistress of the Animals" found on one of the Greek islands (British Museum, 1700-1500 BC, photo.rmn.fr/achats R6NORD24767). N.B. It includes 4 snakes and two birds. Image 9, Tombstone, 400-600 CE (Photo: Gotlands Museum (CC BY 4.0), open woman holding two snakes, crowned with a crown of horns). Image 10, Scythian 11goddess wearing a crown of horns and surrounded by snakes, 300 BC (Photo: Kerch Museum, public domain, 300 BC (Photo: Kerch Museum, public domain).

  One of the Tărtăria tablets with a scene of the domestication of a horned beast depicting a humanoid form with two long arms (Museum of Transylvanian History, Cluj-Napoca, before 5000 BC, public domain); Image 12, Fragment of the ivory handle of a knife (Egypt, Naqada II, 3,300-3,200 BC, Louvre, https://www. photo.rmn.fr/); Image 13, Seal from the Indus Valley (2000-1800 BC, Mohenjo-Daro, photo courtesy of J.M. Kenoyer/Harappa.com); Image 14, Minoan pendant "Mistress of the Animals" (accompanied by 4 snakes and two birds) found on the Greek island -Aegina (British Museum, 1700-1500 BC, photo.rmn.fr/achats R6NORD24767).

  Terracotta (Nagada I), photo courtesy of the National Archaeological Museum of the Netherlands (Rijksmuseum van Oudheden)

  evolution of the concept of the Great Mother Goddess during the last 3,500 years over a vast territory from south to north and from west to east: 14) Figurine 13 , head with bird's profile from the Late Helladic III period (1400-1200 BC, Paris, Musée du Louvre; https://www.photo.rmn.fr) 15) Tombstone, 400-600 CE (Photo: Gotlands Museum (CC BY 4.0), open woman with a crown of horns, holding two snakes); 16) Slavonic embroidery practiced to this day (photo from

On examining the woman's body, the scientists discovered that she had suffered a head injury; as for the man, he had been stabbed in the back with a knife that had pierced his shoulder blade from top to bottom : https://www.britishmuseum.org/blog/virtual-autopsy-discoverhow-ancient-egyptian-gebelein-man-died

2 . As part of an on-going program of reanalysis and conservation, the skin of each Predynastic natural mummy was examined using infrared imaging under both flash and ambient light conditions with a hand-held Panasonic Lumix DMC ZS19 camera, converted to 720 nm infrared by Kolari Vision. Tattoos were detected on the observable areas of the bodies of two individuals(FRIEDMAN & All, 2018: 116-125

).3 The Ramses' period was a period in ancient Egypt, a subdivision of the New Kingdom characterised by the abundance of kings bearing the name of Ramses. It spanned the 19th and 20th dynasties (1296-1069 BC).

. The archaeological culture to which these two tattooed mummies belong. N.B. The Nagada culture (c. 3900-3150 BC) is the most important prehistoric culture in Egypt. It developed over a period of around 750 years in Upper Egypt. At this point, the population evolved from a herding and hunting society, with a few domesticated crops, to a hierarchical society of cereal growers, grouped together in cities and dominated by chiefs, then by rulers who waged war against each other until one of them became pharaoh and united the whole of Egypt under his rule. It was during this final period that Egyptian writing first appeared.

. Bruce Bradley and Dennis JoeStanford ((Standford & Bradley, 2013) are well known for defending the hypothesis of a Solutrean contribution to the Palaeo-Indian settlement of North America. Both argue that the stone tool technology of the Solutrean culture, known in France and Spain towards the end of the Upper Palaeolithic, may have influenced the development of the Clovis culture in America. The lithic tools of these two cultures share many similarities. However, the Solutrean and Clovis cultures are separated by several thousand years.

. The latest information:: http://www.sciencesetavenir.fr/archeo-paleo/homo-sapiens-est-sorti-d-afrique-il-y-a-pres-de-190-000-ans_120243

 7 . In his latest book, "Le Dernier Néandertalien"[START_REF] Slimak | Le Dernier Néandertalien[END_REF] (published on 3 May by Odile Jacob), Ludovic Slimak (archaeologist, researcher at the CNRS and author of several hundred scientific studies) puts forward the idea that the excessive creativity of the Neanderthals worked against them. So, in my opinion, the uniformity of the Sapience culture may have helped them to spread in an extraordinary way, because their cultural code enabled them to recognize each other and therefore not to eliminate each other.

. Archaeologists have discovered more than thirty different visible representations, such as lotus flowers and the eye of Horus, on the skin of a female mummy discovered in the Valley of the Kings, who is thought to have lived during the Ramses' period from 1292 to 1189 BC. Given her tattoos, researchers believe she was a priestess or sorceress with a special connection to the ancient celestial goddess Hathor.

By scanning the man's body, the scientists discovered that he had been stabbed in the back with a knife that crossed his shoulder blade from top to bottom: https://www.britishmuseum.org/blog/virtual-autopsy-discover-how-ancient-egyptian-gebelein-man-died

. In 1704, Leibniz placed the region of origin of the Scythians in the Pontic steppe, making them the ancestors of the Slavs(Demoule, 2015: 27). Today, genetic analyses confirm this in part.

It was not until the Ramses' period (1296-1069 BC) that tattoos were found on a mummified body.

. It reminds us of another "figurine" from Predynastic Egypt (3 500 -3 400 BC) of the culture of Nagada II, currently at the Brooklyn Museum.

. There is a surprising similarity between the first "open women"of the Sahara (Van Albada, 1996 : 1-14), the Egyptian hieroglyph (to beget, to give birth: see the cartridge of Ramses « Re gave birth to him») and Russian letter « ж » : in the archaic Slavic alphabet: 1) Животъ -belly, 2) жизнь во всем своем многообразии жизненных форм -life manifested in every existing creature.


Anthony Streit

Bruno Guillaume
email: bruno.guillaume@efectis.com

Bertrand Girardin

Lucas Terrei

Anthony Collin

Alexis Marchand

Fire propagation from surface to canopy on ornamental species under wind in laboratory conditions

Keywords: Wildfires at Urban Interface, Fire propagation in parcels and structures, Wind-driven laboratory tests, WUI numerical modelling

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

Introduction

Significant efforts have been made to understand the development and expansion of fires at the wildland-urban interface (WUI) (Cohen, 2008;Vacca et al., 2020), showing how the nearest combustible elements to the building are crucial for the propagation of the fire to the building. On the other hand, tree canopy fire contamination in native forests have independently been subject to various studies [START_REF] Rothermel | Predicting behaviour and size of crown fires in the northern Rocky Mountains[END_REF]Fernandes et al., 2009).

At homeowner scale, ornamental vegetation (isolated garden trees, hedges, climbing plants, ...) strongly enhances the danger coming initially from the native forest. In most tests and numerical simulations of WUI fires, these elements, located between the native forest and the building, are generally not represented. However, if represented they burn under very low wind conditions [START_REF] Suzuki | Investigating coupled effect of radiative heat flux and firebrand shower on ignition of fuel beds[END_REF][START_REF] Li | Numerical investigation of the flow characteristics around two tandem propane fires in a windy environment[END_REF]Di Cristina et al., 2021), though in real fires (particularly true in South-East of France), fires in these ornamental elements occur under very gusty and chaotic wind conditions.

This study aims at experimentally reproducing a surface fire (excelsior fuelbed) propagating to a nearby vertical ornamental structure (excelsior and cypress), under high wind exposure (3 m/s) in the laboratory (i.e. at reduced scale). Additionally, a numerical setup composed of the models WFDS/FDS is used to compare and validate the codes against the experimental data. This contribution describes the first steps of this study: the first section describes how zero-wind surface fire experimental data are generated to evaluate the sensitivity of Rate Of Spread (ROS) to fuel load and fuel width. The second section describes the setup of FDS and WFDS models that will be used in the entire study. Then results of some nominal and intermediate model configurations are presented. The last section is dedicated to the intermediate conclusions and to introduce the next steps of the study.

Calibration of the zero-wind surface fire in the experimental setup

The first step consisted in evaluating the ROS of a surface fire under zero-wind condition, in order to gain in reproducibility of surface fires for the full experimental setup. This is a first validation before developing the full experimental setup composed of a surface fire propagating to an ornamental vegetation under high wind exposure (Figure 1b). 85 experiments were performed with zero-wind surface fires [START_REF] Marchand | Fire propagation, Cellular automaton model, Fire front width effect, Radiative transfer[END_REF][START_REF] Marchand | Vegetation fire spread database : 85 wood wool shaving experiments at laboratory scale[END_REF]. They were carried out on excelsior as fuelbed (Figure 1a) and the sensitivity to fuelbed width and fuelbed load was investigated. The combustible material was fully characterised in a previous work by [START_REF] Marchand | Vegetation fire spread database : 85 wood wool shaving experiments at laboratory scale[END_REF]. The first 45 experiments were conducted with a constant vegetation load (0.5 kg/m²) and with fuelbed width ranging from 25 cm to 3.5 m. The excelsior was spread onto the table in order not to exceed a maximum average height of 8.5 cm. The fire was ignited on a line along the whole bed width. The last 40 fire tests were conducted with a constant fuelbed width of 2 m and with a fuel load ranging from 0.1 kg/m² to 1 kg/m². Visible cameras combined with image processing (Otsu algorithm) were used and a direct linear transformation (DLT) algorithm was developed in order to quantify fire behaviour properties (ROS, fire length, etc.). A summary of main results is shown in Figure 2. For the sensitivity of ROS to fuelbed width, ROS is shown to increase at low values of fuel bed width and seems to reach a constant value of about 1.5 cm/s for a 2 m fuel bed width and beyond. In such configurations, the fire fronts are near-parabolic, but the front curvature varies with the line width and the rate of spread is also affected. For the sensitivity to fuelbed load, ROS is shown to globally increase with fuel loads from 0.3 cm/s for the lowest load to 2.6 cm/s in average for the highest load. The repeatability of tests showed discrepancy up to 0.5 cm/s as compared to the average value that can be significant but explained by ambient conditions (different seasons and ambient conditions).

Wind-driven surface fire experiments

A second step consisted in evaluating the ROS of the wind-driven surface fire. Five different wind fans of the "wind wall" were activated with the same constant frequency in each individual experiment. The wind measurements collocated to the fans and at different horizontal distances from the fans, at 0 m and 1m ground heights are shown in Figure 3. The wind at z= 0 m ground height is more affected by the distance to the fans than the wind at z= 1 m. All fan frequencies cannot be used when burning the vegetation since above 30 Hz the excelsior is heavily washed from the table by the wind. Different tests of excelsior burning under different wind speeds have been conducted at two different vegetation loads, set at 0.23 kg/m 2 and 0.4 kg/m 2 . The excelsior fuelbed was positioned at a distance of 1.3 m from the fans.

As shown on Figure 4, the ROS exhibits a strong increase when going from zero-wind to 0.88 m/s wind speed, with a multiplication of ROS by 4 for the 0.23 kg/m 2 case and by 6 for the 0.4 kg/m 2 case. Then a plateau of ROS is observed between 0.88 m/s wind speed and 1.9m/s wind speed and finally another strong ROS increase occurs when reaching 2.4 m/s wind speed. 4. Calibration of the surface and canopy fires, with wind, in the experimental setup Finally, the full experimental setup composed of a surface fire propagating from excelsior to an ornamental vegetation in form of a very thin hedge, with and without wind exposure, has been tested, with the same objective of monitoring ROS.

Two types of vegegation were sampled to constitute the hedge: cypress and oleander. This vegetation was arranged with equal fuel load on a vertical mesh of 1 m large and 1.5 m height, by intertwinning the branches with the fine diameter coarse galvanized steel mesh, which has the advantage of preventing the vegetation from collpasing when burning. A simple evaluation showed that the very fine diameter of the mesh would not modifiy significantly the fire power or the ROS over the hedge. Same fuel load was imposed on the entire mesh with respectively about 1.2 kg/m 2 and 4 cm depth for cypruss and about 1.2 kg/m 2 and 6 cm depth for oleander, collected in gardens and let drying for a minmum of 15 days. Size distribution of <2mm, 2-4 mm, and 4-6 mm diameters were found for cypress of 34.7 %, 55.1%, and 10.2 %. Size distribution of 2-4 mm, 4-6 mm, and 6-8 mm diameters were found for oleander of 48 %, 44 %, and 8 %. The Figure 5 shows cypress and oleander branches and the bulk density evaluation by tube test. The Fuel Moisture Content (FMC) was sampled 1 day before the experiment. FMC of cypress was about 23.8 % on dry matter basis. FMC of oleander was about 10.7 %. The FMC for cypress has been measured 15 times with a SD (standard deviation) of 9.6%, 6 times with a SD of 1.3% for oleander, and 5 times with a SD of 0.7% for excelsior. For ROS measurements, a total of 8 thermocouples (TCs) were vertically-positioned, 4 being vertically aligned along the middle of the hedge and 4 others vertically aligned along the exterior side of the hedge. Each TC is 50 cm distant from another, covering a distance of 0.1 m to 1.6 m over the table. Two visible cameras were also placed, one at the back of the hedge and another one on the side.

A series of 2 experiments were conducted with cypress under zero-wind conditions, while 1 experiment was conducted with cypress under 10 Hz wind conditions (around 0.88 m/s) (outputs not shown here), and 2 experiments were conducted with oleander under zero-wind conditions. Under zero-wind conditions, the fire contaminates the hedge only after the excelsior fire has arrived very close to the foot of the hedge (Figure 6). ROS of the fire in the hedge was quantatively extracted from the vertically-positioned TCs under zero-wind conditions, but the oscillatory flames did contaminate the vertical sensors in an erratic sequence (with higher TCs contaminated prior to lower TCs), preventing from getting the ROS this way. The measurements from visibles cameras revealed a robust way to measure ROS, the imagery being preliminatorily distance-referenced (Figure 7). Cypress fire exhibited ROS values respectively between 35 cm/s and 43 cm/s under zero-wind condition, and 55 cm/s under 10 Hz wind condition. The oleander exhibited ROS values between 22 and 24 cm/s under zero-wind condition. More experiments have been scheduled to gain statistical robusntess of these results. Additionally the calibration of the WFDS and FDS models is in ongoing process on these data. The Fire Dynamic Simulator (FDS) in version 6.7.5 is used here with either (1) a uniform spatial resolution along the three directions of ∆= 2 cm, or (2) with ∆x=∆z =1 cm and ∆y= 2 cm. The pyrolysis and char oxidation processes are driven by an Arrhenius model.

Nominal WFDS and FDS calibration on the intermediate setup of a zero-wind surface fire

The tests modelled with WFDS for the zero-wind surface fire require to attribute values to eight key parameters of the pyrolysis model: the maximum value allowed for the MLR [MLRmax in kg/m 3 /s], the bulk density of vegetation [ρbulk in kg/m 3 ], the density of vegetative fuel [ρ in kg/m 3 ], the surface-to-volume ratio of vegetation [σ in 1/m], the moisture fraction Hu in %wt calculated on a dry mass basis), the fraction of dry virgin vegetation that becomes char τchar (in %wt), the heat of combustion [∆Hr in kJ/kg] and an adimensional multiplicative drag coefficient Cf.

Raw values of these parameters have been previously obtained by [START_REF] Marchand | Vegetation fire spread database : 85 wood wool shaving experiments at laboratory scale[END_REF] and are presented in Table 1. Simulations were made to determine the ROS evolution as a function of the fuelbed width for a 0.5 kg/m² vegetation load using these raw values as input data. Despite that, the global trend is well captured as the ROS increases with the fuel bed width, these simulations exhibited a strong underestimation (60 % differences with the experimental data). Therefore, these values have been fitted: a local sensitivity analysis revealed that MLRmax and ∆Hr were the most significantly sensitive parameters for the ROS predicted by the WFDS model. An identification algorithm (Particle Swarm Optimisation method according to [START_REF] Kennedy | Particle swarm optimization[END_REF]) was then used to identify the best values for these two input parameters, keeping all others at their initial experimental values. As presented in Figure 8, with these new parameters, the numerical trend of ROS with fuelbed width is in a good agreement with the experimental data.

The tests modelled with FDS for the same test configuration require to attribute values to several parameters driving the thermal decomposition and char oxidation. More details about model formulation can be found in [START_REF] Mell | Numerical simulation and experiments of burning douglas fire trees[END_REF][START_REF] Perez-Ramirez | Examination of WFDS in Modeling Spreading Fires in a Furniture Calorimeter[END_REF] and [START_REF] Morandini | Experimental investigation of flammability and numerical study of combustion of shrub of rockrose under severe drought conditions[END_REF] or Porterie et al. (2009). Most of the parameters are extracted from these previous studies. Namely, the parameters describing the dehydration of the vegetation are taken as 𝐸 = 5800𝐾, 𝐴 = 6 × 10 𝑠 𝐾 ⁄ and 𝛥𝐻 = 2.2596 × 10 𝐽. 𝑘𝑔 (endothermic). The parameters describing the decomposition of the vegetation into combustible duel are 𝐸 = 7250𝐾, 𝐴 = 3.63 × 10 𝑠 and 𝛥𝐻 = 1.297 × 10 𝐽. 𝑘𝑔 (endothermic). The latter parameter is the only parameter that is not extracted from [START_REF] Perez-Ramirez | Examination of WFDS in Modeling Spreading Fires in a Furniture Calorimeter[END_REF] or Porterie et al. (2009), its value was fitted so the predicted ROS under zero-wind condition was similar to the experimental one with a fuelbed of 0.5 kg/m² and a fuel width of 0.25 m. The char oxidation model and its inputs was extracted from [START_REF] Perez-Ramirez | Examination of WFDS in Modeling Spreading Fires in a Furniture Calorimeter[END_REF]. Namely, the following parameters were used in our study : 𝐸 = 9000𝐾, 𝐴 = 430 𝑚. 𝑠 and 𝛥𝐻 = 32 × 10 𝐽. 𝑘𝑔 (exothermic). Simulations of FDS conducted with too low fuel loads (0.23 kg/m 2 ) did exhibit no propagation, and calibrating different char oxidation parameters did not change this limiting model behavior. As seen in next section, when using a value of 0.3 kg/m 2 as in [START_REF] Meerpoel-Pietri | Modeling with WFDS Combustion Dynamics of Ornamental Vegetation Structures at WUI: Focus on the Burning of a Hedge at Laboratory Scale[END_REF] did not exhibit this problem.

Nominal FDS simulation on the intermediate setup of a wind-driven surface fire

The configuration of Figure 4 is simulated using the FDS model, using a fuel load of 0.5 kg/m 2 . The model shows a coherent tendency in respect to the observations, with a lower increase of ROS with wind. More experiments at 0.4 kg/m 2 with wind have been scheduled to gain statistical robusntess of these results, to be compared with simulation at 0.4 kg/m 2 . for the experiments, and for one load (0.5 kg/m 2 ) for the model

Nominal FDS simulations in similar setups

A simulation setup is used to illustrate the ability of FDS model to reproduce a zero-wind surface fire, extracted from [START_REF] Meerpoel-Pietri | Modeling with WFDS Combustion Dynamics of Ornamental Vegetation Structures at WUI: Focus on the Burning of a Hedge at Laboratory Scale[END_REF] referred hereafter as MP2022, with additional 20 % slope of the fuelbed. The fuelbed is also there composed of excelsior. The configuration from MP2022 as well as the input values given by the authors for the Arrhenius pyrolysis model are used within the FDS model, while the authors used the WFDS model.

As shown in Figure 10, the FDS outputs have a very similar intensity curve as the WFDS at 2 cm resolution from MP2022 , while being globally 22 % higher in intensity in the period between 5 s and 77 s. The difference in terms of intensity may be explained by the difference of the two codes. However, the ROS is coherent with the WFDS results and with the experimental data. A second similar setup as the full ornamental vegetation setup of this study is the single-tree canopy fire under zero wind provided by [START_REF] Mell | Numerical simulation and experiments of burning douglas fire trees[END_REF], referred hereafter as M2009. The Mass Loss Rates (MLR) are calculated with FDS in this study for two different grid resolution, 10 cm and 25 cm, together with two different pyrolysis schemes: Arrhenius (same scheme as in the previous nominal zero-wind surface fire test) and simplified Arrhenius (scheme from older FDS versions). As shown in Figure 11 for a 5 m tree, the M2009 WFDS simulation is the closest to the experimental data, but all simulations from our study vary here only with a delay of less than 5 seconds in the peak MLR value, and with less than 20 % difference in peak value.

Conclusions

Based on experimental data on zero-wind surface fire propagation, this contribution showed promising results on the ability of WFDS and FDS to reproduce well the fire front behaviour. Moreover, the ability of FDS to propagate to an isolated vertical tree with the same modelling processes is also presented and validated.

A new experimental setup allowing simulating a scenario of fire contamination from the surface to an ornamental vegetation, under high wind conditions, is in ongoing development. It involves a surface fire scenario, represented by a fire in Excelsior, which contaminates an ornamental vegetation. Some targeted nominal intercomparisons with the WFDS and FDS models will be presented in the final contribution. This new experimental setup will allow in a coming future to evaluate the impact of vertical discontinuities (low branches position of the ornamental vegetation), as well as effect of wind intermittency.

Benichou N., Adelzadeh M., Singh J., Gomaa I., Elsagan N., Kinateder M., Ma C., Gaur A., Bwalya A.

Figure 1 -

 1 Figure 1 -Zero-wind fire spread test on the surface fuelbed, (b) View of the high wind exposure facility

Figure 2 -

 2 Figure 2 -Distribution in the 85 experiments of the rate of spread as a function of fuelbed width (red colour) for a constant vegetation load of 0.5 kg/m² and as a function of fuelbed load (green colour) for a constant fuelbed width set at 2 m.

Figure 3 -

 3 Figure 3 -Wind speed wih horiztonal distance to the fans, and at two different ground heights (z=0m and z=1m)

Figure 4 -

 4 Figure 4 -Rates of spread in function of the wind speed for two different loads (0.2 kg/m 2 and 0.4 kg/ m 2 )

Figure 5 -

 5 Figure 5 -Property measurements: (left) oleander weighting, (middle) cypress branches clustering for size distribution evaluation, (right) cypress bulk density evaluation

Figure 6 -

 6 Figure 6 -Fire contamining from excelsior fire to the hedge under zero-wind conditions, (upper) for cypress and (lower) for oleander. Propagation visualized in 5 phases (from left to right): excelsior fire approaches, excelsior fire at the foot of the hege (reference time t=0s), fire at maximum development in the hedge, fire largely decreasing, fire in extinction phase

Figure 7 -

 7 Figure 7 -Zero-wind condition cypress ROS measured by manual interpretation on distance-referenced thermal camera imagery

Figure 9 -

 9 Figure 9 -Comparison of rates of spread varied with wind intensity, for two different loads (0.2 kg/m 2 and 0.4 kg/m 2 )for the experiments, and for one load (0.5 kg/m 2 ) for the model

Figure 10

 10 Figure 10. (upper row): Comparison of the intensity-time curves: the WFDS 1 cm and 2 cm and the experimental data are taken from MP2022 while the FDS is from current study, (lower row): Comparison in side view along the full slope of the observed (left) and modelled (right) flame height at timestep 51 s (source: observed flame photo is from Meerpoel Pietri et al. (2022))

Figure 11 -

 11 Figure 11 -Time evolution of MLR in current FDS version with both pyrolysis schemes and both resolutions (10 cm and 25 cm), compared with the Mell et al. (2009) experiment data and numerical WFDS outputs These nominal simulations of FDS based on current state model should be confronted with observations of next coming surface and canopy fire tests in the study.

  , and Sultan M. (2021). National Guide for Wildland-Urban Interface Fires. National Research Council Canada: Ottawa, ON. 192 pp Cohen J (2008) The wildland-urban interface fire problem: A consequence of the fire exclusion paradigm. Forest History Today. Fall: 20-26. Di Cristina G., Kozhumal S., Simeoni A., Skowronski N., Rangwala A.; Im, S.-K. (2021)doi.org/10.1016/j.firesaf.2020.103090. Fernandes P.-M. (2009). Combining forest structure data and fuel modelling to classify fire hazard in Portugal. Annals of Forest Science, Springer Nature (since 2011)/EDP Science (until 2010), 66 (4).

Table 1 -

 1 Input parameters used for WFDS: comparison between raw experimental values and fitted optimised values

	Features	Initial experimental values	Fitted Optimal values
	MLRmax [kg/m 3 /s]	0.22	0.43
	ρbulk [kg/m 3 ]	5.55
	ρ [kg/ m3 ]	519
	σ [1/m]	14 600
	Hu [-]	0.12
	τchar [-]	0.31
	∆Hr [kJ/kg]	16 480	14 497
	Cf [-]	0.375

Figure 8 -Results of the two sets of WFDS simulations of ROS, with raw experimental values of the pyrolysis model parameters, and fitted optimal values

10Hz, z= 0m 10Hz, z= 1m 20Hz, z= 0m 20Hz, z= 1m 30Hz, z= 0m 30Hz, z= 1m 40Hz, z= 0m 40Hz, z= 1m


Abdelghani Maddi
email: abdelghani.maddi@cnrs.fr

The Nexus of Open Science and Innovation: Insights from Patent Citations

Keywords: Open Access, Innovation, Non-Patent References, Patents, OpenAlex, NOAI

This paper aims to analyze the extent to which inventive activity relies on open science. In other words, it investigates whether inventors utilize Open Access (OA) publications more than subscription-based ones, especially given that some inventors may lack institutional access. To achieve this, we utilized the (Marx, 2023) database, which contains citations of patents to scientific publications (Non-Patent References -NPRs). We focused on publications closely related to invention, specifically those cited solely by inventors within the body of patent texts. Our dataset was supplemented by OpenAlex data. The final sample comprised 961,104 publications cited in patents, of which 861,720 had a DOI. Results indicate that across all disciplines, OA publications are 38% more prevalent in patent citations (NPRs) than in the overall OpenAlex database. In biology and medicine, inventors use 73% and 27% more OA publications, respectively, compared to closed-access ones. Chemistry and computer science are also disciplines where OA publications are more frequently utilized in patent contexts than subscription-based ones.

Introduction

Innovation is the cornerstone of societal progress, propelling advancements in technology, economy, and scientific understanding (de las [START_REF] De Las Heras-Rosas | Research Trends in Open Innovation and the Role of the University[END_REF][START_REF] Jefferson | Mapping the global influence of published research on industry and innovation[END_REF]. At the heart of this dynamic landscape lies the concept of open science, which advocates for unrestricted access to research findings and collaborative sharing of knowledge [START_REF] Hecker | Citizen Science: Innovation in Open Science[END_REF]. Open science represents a departure from traditional closed models of scientific dissemination, aiming to democratize access to information and accelerate the pace of discovery. Within the realm of open science, one crucial aspect deserving closer examination is the accessibility of scientific publications. Open Access (OA) to research articles has become increasingly prevalent, facilitated by initiatives such as institutional repositories, preprint servers, and open access journals. This shift towards OA has been lauded for its potential to democratize knowledge, remove barriers to information, and foster collaboration among researchers worldwide [START_REF] Robinson-Garcia | Open Access uptake by universities worldwide[END_REF].

Despite the considerable attention paid to the benefits of open science, its specific impact on innovation remains relatively underexplored [START_REF] Jahn | Quantifying the influence of Open Access on innovation and patents[END_REF]. While open science initiatives strive to enhance transparency, reproducibility, and collaboration in research endeavors, the extent to which these principles translate into tangible advancements in inventive activity is less understood. This gap in understanding prompts a critical inquiry into the relationship between open access publications and inventive endeavors. Patent citations serve as a tangible indicator of the scientific knowledge base underpinning technological innovation. Known as Non-Patent References (NPRs), these citations provide insights into the sources of information and inspiration driving inventive activity. By analyzing the prevalence and utilization of open access publications within patent citations, we can gain valuable insights into the role of open science in shaping innovative processes.

In this paper, we aim to address this gap in knowledge by conducting a comprehensive analysis of patent citations across various disciplines. Leveraging data from the database curated by [START_REF] Marx | Reliance on Science[END_REF], supplemented by OpenAlex data, we focus on discerning patterns and trends in the citation of open access versus subscription-based publications. Specifically, we seek to answer key questions such as whether inventors exhibit a preference for open access publications, how this preference varies across disciplinary boundaries, and what implications these findings hold for the promotion of open science and innovation.

In contrast to the study conducted by [START_REF] Jahn | Quantifying the influence of Open Access on innovation and patents[END_REF], which encompasses all Non-Patent References (NPRs), including those not directly related to the invention or introduced by examiners, our study focuses specifically on NPRs cited by inventors themselves and within the body of the invention text. Moreover, our analysis introduces the use of the normalized indicator NOAI (Normalized Open Access Index) to account for disciplinary disparities. This approach allows for a more nuanced understanding of the utilization patterns of open access publications within the context of patent citations, taking into consideration disciplinary differences and providing insights into the reliance on open access literature across various fields of research.

Through our investigation, we endeavor to contribute to a deeper understanding of the mechanisms driving innovation in the 21st century and the role of open science therein. By shedding light on the relationship between open access publications and inventive activity, we aim to inform policy discussions, scholarly discourse, and practical strategies aimed at fostering a more open and collaborative research ecosystem. Ultimately, our findings aspire to empower stakeholders with actionable insights to leverage open science principles for stimulating innovation and addressing societal challenges.

Data

This study relies on data provided by [START_REF] Marx | Reliance on Science[END_REF], which includes a vast collection of 6 million scientific publications cited in patents, focusing on what are called Non-Patent References (NPRs). This dataset is unique because it distinguishes between references cited by examiners and those cited by inventors (applicants). Additionally, it provides information on where each citation is located within the patent text (front page, body, or both), giving us valuable context.

To focus our analysis, we selected publications cited in the body of patent texts by applicants. This choice was made because citations on the front page of patents, especially in the U.S. Patent and Trademark Office (USPTO), are often added by examiners and may not directly reflect the inventors' contributions. Research has shown that citations made by inventors within the body of the patent text, which describe the invention in detail, are the most relevant to the innovation process [START_REF] Bryan | In-text patent citations: A user's guide[END_REF][START_REF] Quemener | Technological impact of funded research: A case study of non-patent references[END_REF].

To enrich our analysis, we used the OpenAlex API (https://docs.openalex.org/) to gather additional metadata from these publications. This included information about the specific domains (referred to as "concepts" in OpenAlex) within the highest-level aggregation, which encompasses 19 domains. OpenAlex assigns each article one or more concepts with a relevance score ranging from 0 to 1. We considered all concepts with a non-zero score. Additionally, we calculated a fractional count to measure the weight of each discipline based on the score developed by [START_REF] Klebel | The APC-barrier and its effect on stratification in open access publishing[END_REF].

Our final dataset comprises 961,069 publications cited in patents, with 861,729 having a DOI. This sample size ensures the reliability of our analysis and provides meaningful insights into the use of open access publications in inventive activity.

Methods

To assess the extent to which OA publications are more or less concentrated among patent citations, we employed a method based on the double ratio, as outlined in [START_REF] Maddi | Measuring open access publications: A novel normalized open access indicator[END_REF] study. This double ratio is formalized as the Normalized Open Access Index (NOAI), which compares the proportion of OA publications within each discipline among patent citations to the corresponding proportion in the entire OpenAlex database. Specifically, the NOAI is calculated by dividing the proportion of OA publications in a given discipline among patent citations by the same proportion in the entire OpenAlex database. Thus, a NOAI greater than 1 indicates an over-representation of OA publications among patent citations for that discipline, while a NOAI less than 1 suggests under-representation.

For example, if the NOAI for a particular discipline is 1.3, it signifies that OA publications are cited in patents 30% more frequently than the average for OA publications in the entire OpenAlex database. Conversely, a NOAI of 0.8 would indicate that OA publications are less frequently cited in patents within that discipline compared to the overall average for OA publications. This approach enables us to quantitatively and comparatively understand the concentration of Open Access publications within the inventive activity, highlighting differences in the representation of OA publications among patents across disciplines.

Results

This section comprises two main parts aimed at providing an understanding of the utilization patterns of Non-Patent References (NPRs) across various disciplines. Firstly, we present descriptive statistics regarding the distribution of NPRs by discipline, shedding light on the prevalence of these references within different fields of research. Secondly, we delve into the outcomes of calculating the Normalized Open Access Index (NOAI).

descriptive statistics

Table 1 provides a significant insight into the utilization of Non-Patent References (NPRs) across various disciplines, along with comparisons between the rates of Open Access (OA) publications within the NPRs dataset and the entire OpenAlex database.

Firstly, examining the distribution of the total number of NPR publications by discipline reveals substantial variation. Disciplines such as Biology, Chemistry, and Medicine stand out with higher numbers of NPRs, representing 26.8%, 23.0%, and 16.4% of the total NPRs, respectively. However, some disciplines, such as Art, History, Geography, and Sociology, are less represented, each accounting for less than 1% of the total. This disparity was to be expected, as NPRs are publications cited in patents, meaning they are cited based on the specific application domains of patents. Thus, disciplines less directly related to technical or industrial applications may naturally be less frequently cited in patents.

Secondly, the comparison of OA rates between the NPRs dataset and the entire OpenAlex database reveals interesting trends. While the overall OA publication rate in OpenAlex is 21.4%, the OA rate within the NPRs dataset is significantly higher, reaching 32.4%. This suggests that NPRs have a higher propensity to include OA publications compared to the entire database. However, it is important to note that this trend varies by discipline. For example, Medicine displays an OA rate of 36.1% in the NPRs dataset, while Philosophy has a much lower OA rate of 15.9%. This disparity underscores the importance of considering disciplinary specificities when analyzing the use of OA publications in NPRs. Furthermore, it's worth noting a curious result observed in Material Science and Physics where the OA rate within NPRs is lower than the OpenAlex average. These cases merit further investigation as they deviate from the general trend observed across disciplines.

Normalized Open Access Index

The value of the Normalized Open Access Index (NOAI) for all disciplines combined is calculated by taking the weighted average of the NOAI values for each discipline. In this regard, the overall NOAI is established at In addition to the analysis presented, it would be intriguing to incorporate consideration of "black open access" (OA) sources, such as those accessible through platforms like Sci-Hub.

Integrating black OA into the analysis could provide further insights into the accessibility and reliance on open access literature within different disciplines. Given the controversial nature of black OA and its potential impact on traditional publishing models, examining its influence on the Normalized Open Access Index (NOAI) could offer a more comprehensive understanding of scholarly communication practices.

Understanding how black OA sources contribute to the availability and utilization of research literature could reveal whether the NOAI values would be even higher than observed. This exploration could shed light on the extent to which applicants rely on alternative means to access scholarly content, particularly in disciplines where access barriers are more pronounced. Furthermore, it could prompt discussions on the efficacy of traditional publishing models and the role of black OA in democratizing access to knowledge.

Discussion

The salient revelation of this study is that OA publications are more prevalent in patent citations compared to the overall OpenAlex database.

Conclusion

This study aimed to analyze the extent to which inventive activity relies on open science, particularly focusing on the utilization of Open Access (OA) publications within patent citations. Leveraging data from the [START_REF] Marx | Reliance on Science[END_REF] database, encompassing citations of patents to scientific publications (Non-Patent References -NPRs), and supplemented by OpenAlex data, our analysis provides valuable insights into the relationship between open science and innovation.

The finding that OA publications are more prevalent in patent citations than in the overall OpenAlex database underscores the significant impact of open science on inventive activity. Across all disciplines, OA publications are 38% more prevalent in patent citations (NPRs) than in the entire OpenAlex database, indicating a pronounced preference among inventors for utilizing openly accessible scientific literature in their innovative endeavors.

The substantial prevalence of OA publications, particularly evident in disciplines such as biology, medicine, chemistry, and computer science, reflects the increasing recognition of the value and relevance of open access resources in driving technological innovation. This trend

Figure 1 :

 1 Figure 1 : Normalized Open Access Index by discipline (only publications with DOI) 1,73

Table 1 : Distribution of Non-Patent References -NPRs, by OpenAlex domains, fractional counting

 1

	Discipline	NPRs -Non-OA	NPRs -OA	# in NPRs dataset	% in NPRs dataset	% OA in NPRs	% OA in all OpenAlex database
	Biology	109 193.79 121 893.04 231 086.84	26.8%	52.7%	30.4%
	Chemistry	145 082.55 52 862.01 197 944.55	23.0%	26.7%	23.7%
	Medicine	90 432.60 51 085.19 141 517.78	16.4%	36.1%	28.4%
	Computer science	72 385.94 17 617.05 90 002.99	10.4%	19.6%	18.2%
	Materials science	66 965.56 12 159.08 79 124.64	9.2%	15.4%	21.2%
	Physics	24 394.83	6 639.40 31 034.24	3.6%	21.4%	24.6%
	Mathematics	12 183.89	4 308.57 16 492.46	1.9%	26.1%	27.2%
	Psychology	12 411.54	3 328.04 15 739.58	1.8%	21.1%	23.5%
	Engineering	11 733.82	1 962.80 13 696.62	1.6%	14.3%	21.1%
	Political science	5 249.49	998.41	6 247.90	0.7%	16.0%	18.1%
	Philosophy	4 815.92	911.86	5 727.78	0.7%	15.9%	20.5%
	Geology	4 417.90	1 026.32	5 444.22	0.6%	18.9%	19.6%
	Environmental science	4 068.24	1 166.25	5 234.49	0.6%	22.3%	23.0%
	Art	4 290.73	625.46	4 916.18	0.6%	12.7%	17.0%
	History	4 091.92	528.79	4 620.71	0.5%	11.4%	12.4%
	Business	2 967.66	712.52	3 680.18	0.4%	19.4%	18.1%
	Geography	2 848.64	811.28	3 659.92	0.4%	22.2%	21.3%
	Sociology	2 910.41	409.57	3 319.99	0.4%	12.3%	23.7%
	Economics	1 827.57	401.35	2 228.93	0.3%	18.0%	23.5%
	Total	582 273.00 279 447.00 861 720.00 100.0%	32.4%	21.4%

  1.38. This value signifies that, on average, open access (OA) publications are 38% more prevalent in Non-Patent References (NPRs) than in the entire OpenAlex database. It suggests that NPRs have a higher propensity to include OA publications compared to the entire database, thus demonstrating a pronounced preference for open access to scientific literature among patent citations. The global NOAI value highlights the growing importance of open access in the research and innovation landscape, emphasizing the need to encourage and promote policies and practices that foster accessibility and dissemination of scientific knowledge. Figure 1 presents the distribution of the Normalized Open Access Index (NOAI) across different disciplinary domains, focusing on publications with Digital Object Identifiers (DOIs). The NOAI values, ranging from 0.52 to 1.73, provide insights into the relative prevalence of Open Access (OA) publications within patent citations across various disciplines. Several noteworthy trends emerge from the data. Disciplines such as Biology, Medicine, and Chemistry exhibit relatively high NOAI values, indicating a substantial reliance on open access literature within these fields. Conversely, disciplines like Sociology, Engineering, and Materials Science demonstrate lower NOAI values, suggesting a comparatively lower dependency on open access publications, even when considering those with DOIs. Interestingly, disciplines like Computer Science and Business present NOAI values that are higher than the average, despite their relatively lower shares of open access publications within the NPRs dataset.

  This finding not only illuminates the symbiotic relationship between open science and inventive activity but also highlights the transformative potential of open access resources in driving technological innovation. It presents a novel insight into the utilization patterns of OA literature by inventors, reflecting a paradigm shift towards leveraging openly accessible scientific knowledge in the inventive process.Our results are consistent with previous research.[START_REF] Bryan | The Impact of Open Access Mandates on Invention[END_REF] found a slight increase in citations to NIH-funded research following the NIH Open Access policy implementation, particularly benefiting small biotechnology companies. Similarly,[START_REF] Jahn | Quantifying the influence of Open Access on innovation and patents[END_REF] discovered that approximately one third of patent families referenced non-patent literature, with a growing proportion of Open Access citations over time. These findings support the growing importance of Open Access in facilitating access to scientific knowledge and driving innovation.The implications of these findings extend beyond academia, carrying significant political ramifications. The observed disparities in OA usage among different fields underscore the need for targeted policy interventions to promote open access awareness and enhance the visibility of OA resources. Policymakers can leverage these insights to formulate strategies aimed at fostering a more inclusive and collaborative research environment, ultimately driving societal progress and economic development.Additionally, the pronounced preference for OA publications in patent citations signals a shift towards a more open and transparent innovation ecosystem. This presents an opportunity for policymakers to enact policies that incentivize the adoption of open science practices and promote equitable access to scientific knowledge. By fostering a culture of openness and collaboration, policymakers can stimulate innovation, accelerate scientific progress, and address societal challenges more effectively.