Thierry Douki
email: thierry.douki@cea.fr

Daniel Bacqueville

Carine Jacques

Camille Geniès

Nicolas Roullet

Sandrine Bessou-Touya

Hélène Duplan

Blue light impairs the repair of UVB-induced pyrimidine dimers in a human skin model

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

INTRODUCTION

Ultraviolet (UV) irradiation leads to harmful effects including skin aging and skin cancer due to increased production of cellular reactive oxygen species and by direct DNA damage. Damaged DNA, if not properly repaired, is a source of mutations, and interferes with many cellular mechanisms such as replication, transcription, and cell cycle. Recent studies have highlighted the impact of the visible light on the skin. An action spectrum of visible light in HaCat keratinocytes showed that the deleterious effect decreased in the order violet > blue > green > red [START_REF] Tonolli | The phototoxicity action spectra of visible light in HaCaT keratinocytes[END_REF]. These observations demonstrate the major role played by high-energy visible light spectral range (400-450 nm). Large amounts of information have been in particular gathered on blue light (BL) and revealed damaging effects on cutaneous cells mainly by inducing an oxidative stress. In keratinocytes cultured in vitro, violet and BL have been shown to induce oxidative stress, mitochondrial dysfunctions and blockade of autophagy and DNA damage [START_REF] Nakashima | Blue light-induced oxidative stress in live skin[END_REF][START_REF] Tonolli | The phototoxicity action spectra of visible light in HaCaT keratinocytes[END_REF][START_REF] Chamayou-Robert | Blue light induces DNA damage in normal human skin keratinocytes[END_REF]. Similar observations were made in melanocytes [START_REF] Zhou | Low energy multiple blue light-emitting diode light Irradiation promotes melanin synthesis and induces DNA damage in B16F10 melanoma cells[END_REF]. Another interesting feature of visible light is that it is more abundant and penetrates deeper into the skin layers than UV. BL have been implicated in erythema, hyperpigmentation and premature skin aging [START_REF] Narla | Visible light in photodermatology[END_REF][START_REF] Schutz | Blue Light and the Skin[END_REF][START_REF] Coats | Blue light protection, part II-Ingredients and performance testing methods[END_REF][START_REF] Passeron | Photoprotection according to skin phototype and dermatoses: practical recommendations from an expert panel[END_REF][START_REF] Bacqueville | Formulation of a new broad-spectrum UVB + UVA and blue light SPF50(+) sunscreen containing Phenylene Bis-Diphenyltriazine (TriAsorB), an innovative sun filter with unique optical properties[END_REF]. Induction of oxidative stress is also documented [START_REF] Nakashima | Blue light-induced oxidative stress in live skin[END_REF]. This evidence that BL is active in skin raises the concern about a possible worsening impact of BL on effect of UV.

A major issue in the deleterious effect of sunlight is its genotoxicity, which is directly linked to induction of skin cancer. In vitro, BL has been shown to damage DNA by oxidation processes [START_REF] Kielbassa | Wavelength dependence of oxidative DNA damage induced by UV and visible light[END_REF][START_REF] Kvam | Induction of oxidative DNA base damage in human skin cells by UV and near visible radiation[END_REF][START_REF] Tonolli | The phototoxicity action spectra of visible light in HaCaT keratinocytes[END_REF][START_REF] Chamayou-Robert | Blue light induces DNA damage in normal human skin keratinocytes[END_REF]. The latter are triggered by BL mediated photosensitization reactions involving endogenous chromophores [START_REF] Nakashima | Blue light-induced oxidative stress in live skin[END_REF][START_REF] De Assis | How does the skin sense sun light? An integrative view of light sensing molecules[END_REF]. Superoxide anion is the main species produced (2), likely through excitation of flavins [START_REF] Imlay | Pathways of oxidative damage[END_REF]. BL has also been shown to induce chromosome aberrations in vitro [START_REF] Chamayou-Robert | Blue light induces DNA damage in normal human skin keratinocytes[END_REF]. BL-induced DNA damage is yet approximately 3 orders of magnitude less efficient at damaging DNA than UVB at inducing cyclobutane pyrimidine dimers (CPDs) [START_REF] Kielbassa | Wavelength dependence of oxidative DNA damage induced by UV and visible light[END_REF][START_REF] Kvam | Induction of oxidative DNA base damage in human skin cells by UV and near visible radiation[END_REF]. More recently, a study on human volunteers showed that the induction of dark CPDs was efficient at 380 nm but not in the visible light range [START_REF] Lawrence | The UV/visible radiation boundary region (385 -405 nm) damages skin cells and induces "dark" cyclobutane pyrimidine dimers in human skin in vivo[END_REF]. These results strongly suggest that the DNA damage induced by BL do not significantly contribute directly to the initiation of skin cancer.

However, BL may be indirectly genotoxic by preventing the repair of DNA damage induced by other wavelengths ranges, especially carcinogenic UVB.

In order to test this hypothesis, we designed a realistic protocol where reconstructed human epidermis (RHE) were first exposed to BL and then to UVB. We further took advantage of the photoprotective efficacy against BL of the new sunfilter Phenylene Bis-Diphenyltriazine (TriAsorB ® ) to unambiguously establish the role of BL. This organic sunscreen has a critical wavelength ≈ 390 nm. The filter effectively absorbs visible light especially in the region from 400 to 450 nm bandwidth. The absorbance decreases with increasing wavelength and dropped at about 0.1 at 450 nm with a λVis-CW =594 nm [START_REF] Bacqueville | Phenylene Bis-Diphenyltriazine (TriAsorB), a new sunfilter protecting the skin against both UVB plus UVA and blue light radiations[END_REF]. Moreover, TriAsorB is also able to reflect BL with a peak of reflectance at about 450 nm and a progressive decrease up to 700 nm [START_REF] Bacqueville | Phenylene Bis-Diphenyltriazine (TriAsorB), a new sunfilter protecting the skin against both UVB plus UVA and blue light radiations[END_REF]. Its filtering efficacy against BL radiations has been demonstrated by inhibition of the formation of 8-oxo-7,8-dihydroguanine in reconstructed human skin after exposure to 80 J.cm -2 of BL at 427±30 nm. Moreover, TriAsorB formulation as a SPF50 + sunscreen in combination with other UV filters prevented cellular photodamage and BL-induced oxidatively generated DNA lesions [START_REF] Bacqueville | Formulation of a new broad-spectrum UVB + UVA and blue light SPF50(+) sunscreen containing Phenylene Bis-Diphenyltriazine (TriAsorB), an innovative sun filter with unique optical properties[END_REF].

GRAPHICAL ABSTRACT

Exposure of reconstructed human epidermis with blue light decreases the rate of repair of pyrimidine dimers induced in DNA by a subsequent UVB irradiation. This deleterious effect is prevented by application of a sunscreen exhibiting blue light photoprotection.

UVB Blue light

MATERIALS AND METHODS

TriAsorB and SPF50 + sunscreen formulations

The commercially available SPF50 + sunscreen containing TriAsorB

Growth of reconstructed human epidermis

In this study, the model used was a follicular model of RHE in vitro. The epidermis was reconstructed from keratinocytes derived from the outer epithelial sheath of human hair follicles obtained from healthy volunteers who had given informed consent. The 3D reconstruction method was previously described by Guiraud et al. ( 16) and Bacqueville et al. [START_REF] Bacqueville | A new hair follicle-derived human epidermal model for the evaluation of sunscreen genoprotection[END_REF]. The outer epithelial sheath cells of human hair follicles are a readily available and non-invasive source of keratinocytes for epidermal reconstruction. Briefly, the cells were isolated from the outer epithelial sheath of the hair follicles and then cultured before seeding on culture inserts (CLS3460, Corning ® ) immersed in culture medium. The culture inserts are then placed at the air/liquid interface in an incubator at 37°C with 5% CO2 to induce epidermal differentiation and maturation of the stratum corneum. The culture medium is renewed every 24 hours.The RHE is formed in 16 days with a surface area of 1.12 cm².

Blue light and UVB irradiations of skin model

TriAsorB and SPF50 + sunscreen formulations were evaluated for BL photoprotection. They were applied at a dose of 2 mg.cm -² to the surface of a polymethyl methacrylate (PMMA) plate.

This plastic is naturally transparent and has greater light transmission than glass. The PMMA plate is then deposited on the RHE model just before exposure to BL radiation using a blue light LED lamp (Kessil PR160) [START_REF] Bacqueville | Phenylene Bis-Diphenyltriazine (TriAsorB), a new sunfilter protecting the skin against both UVB plus UVA and blue light radiations[END_REF][START_REF] Bacqueville | Formulation of a new broad-spectrum UVB + UVA and blue light SPF50(+) sunscreen containing Phenylene Bis-Diphenyltriazine (TriAsorB), an innovative sun filter with unique optical properties[END_REF]. The power of the LED lamp is 257.4 W.m -² and the wavelength is 427±30 nm. The RHE models were exposed to BL at a dose of 60 or 92 J.cm -² for a duration of 39 min and 1 hour, respectively.

After this BL stress, the PMMA plate was removed and the skin was then exposed to UVB by using a Biosun RMX irradiator (Vilber Lourmat, Germany) equipped with a monochromatic illumination lamp at 312 nm. The lamp power is approximately 3 mW.cm -2 . RHE models were exposed to a single dose of 50 mJ.cm -². To assess DNA repair, tissues were finally harvested just after UVB exposure (t0) or 48 hours after the UVB stress (t48h), and all were frozen at -80°C before analysis by liquid chromatography coupled to tandem mass spectrometry (HPLC-MS/MS).

All experiments were performed in 3 independent biological replicates (N=3) with n=3 or 4

technical replicates for each series (n=3), except for the conditions UVB stress alone (UVB control) and BL stress plus UVB stress (BL + UVB) (N=6, n=3 or 4).

DNA extraction and quantification of photoproducts

DNA was then extracted from the RHE with the DNeasy tissue kit (Qiagen) following the manufacturer instructions. Briefly, samples were grinded in a tissue lyzer with steel beads in buffer ATL. Samples were then incubated for 3 h at 55°C in the presence of proteinase K, followed by a RNA treatment for 2 min. The lysis was completed by a 10 min incubation at 70°C with AL buffer. Ethanol was added and DNA trapped on silica gel column. It was washed twice and finally collected in water. The recover fraction was freeze-dried. The residue obtained was enzymatically hydrolyzed and analyzed by HPLC-MS/MS as previously reported [START_REF] Douki | The variety of UV-induced pyrimidine dimeric photoproducts in DNA as shown by chromatographic quantification methods[END_REF].

Statistical analyses

Non-parametric analyses were performed on the Prism-GraphPad software (San Diego, CA). A Kruskall-Wallis multiple comparison was first performed. It was followed by comparison between selected conditions by use of a post-hoc Dunn test. Reported results are median ± 25 th -75 th percentiles range.

RESULTS

Quantification of photoproducts after UVB and Blue light + UVB exposure

Cyclobutane pyrimidine dimers (CPDs) and pyrimidine (6-4) pyrimidone photoproducts (64PPs) were quantified in the DNA of RHE collected either immediately (t0) or 48 hours after irradiation (t48h) (Table 1). No photoproduct was detected in the DNA of unirradiated RHE or exposed only to BL. The distribution of photoproducts at t0 just after UVB exposure was similar to previous results: i) CPDs are 3 times more frequent than 64PPs, ii) the order of formation of CPDs is TT > TC > CT, iii) TC 64PP is more frequent than TT 64PP and iv) very little Dewar valence isomers are produced with UVB [START_REF] Douki | Bipyrimidine photoproducts rather than oxidative lesions are the main type of DNA damage involved in the genotoxic effect of solar UVA radiation[END_REF][START_REF] Mouret | Cyclobutane pyrimidine dimers are predominant DNA lesions in whole human skin exposed to UVA radiation[END_REF]. The observations at t48h for DNA repair after pure UVB are also those expected, namely that 64PPs are removed from DNA faster than CPDs [START_REF] Mitchell | 6-4) Photoproducts are removed from the DNA of UV-irradiated mammalian cells more efficiently than cyclobutane pyrimidine dimers[END_REF][START_REF] Young | The in situ repair kinetics of epidermal thymine dimers and 6-4 photoproducts in human skin types I and II[END_REF][START_REF] Courdavault | Repair of the three main types of bipyrimidine DNA photoproducts in human keratinocytes exposed to UVB and UVA radiations[END_REF][START_REF] Mouret | Differential repair of UVB-induced cyclobutane pyrimidine dimers in cultured human skin cells and whole human skin[END_REF]. In addition, not all CPDs were repaired with the same efficiency. The decreasing order of removal rate was CT> TC > TT [START_REF] Mouret | Differential repair of UVB-induced cyclobutane pyrimidine dimers in cultured human skin cells and whole human skin[END_REF]. BL exposure at either 60 or 92 J.cm -2 before UVB irradiation did not affect the level of photoproducts quantified at t0 as inferred from the absence of statistically significant differences. Interestingly, the frequency of pyrimidine dimers was lower 48h post-exposure. These differences were statistically significant for 64PPs under all conditions and for CPDs after pure UVB irradiation. However, statistical significance was not reached for samples exposed to BL before UVB.

Effect of blue light on DNA repair

For a better assessment of the impact of BL on DNA repair, repair efficiency was calculated for each value. Equation (1) was used:

(1) % repair = 100 * (average(dimer t0 ) -dimer t48h )/average(dimer t0 )

where average(dimert0) is the average of the level of a photoproduct under specific conditions at t0, dimert48h is a value of the level of the same photoproduct and conditions at 48h, and %repair is the index of repair efficiency.

The %repair parameter was calculated for all individual photoproducts (Table 2) as well as for the sum of either all CPDs or all 64PPs (Fig. 1) following the exposure to pure UVB, BL 60 J.cm -2 + UVB and BL 92 J.cm -2 + UVB. A statistically significant decrease in the repair efficiency was observed in all cases, whatever the BL dose applied before UVB irradiation. Remarkably, the deleterious effects of BL on DNA repair were even observed for 64PPs that are very efficiently excised. The differences between %repair for the 60 and 92 J/cm 2 BL treatments did not reach statistical significance.

Photoprotection against BL-induced DNA repair impairment

Quantification of DNA repair was then performed with BL-absorbing/reflecting sunscreens spread on a PMMA plate, placed above the RHE only during the BL irradiation. Data were obtained with BL at the 60 J.cm -2 dose. Both a TriAsorB 5% formulation and a commercial SPF50 + sunscreen containing this UVB + UVA + BL filters were investigated for their photoprotective properties against the deleterious effects of BL radiations on DNA repair. A significant improvement of DNA repair was observed for sunscreen formulations. This was well shown for the DNA repair of TT CPD and the combination of all CPDs (Fig. 2) for which the efficiency of repair was doubled by using a photoprotection during BL exposure. A protective effect was also observed for TC CPD with both formulations. Interestingly, a positive effect of TriAsorB 5% was observed for either TT 64PP or all 64PPs combined.

Figure 1 .

 1 Figure 1. %repair of A) all CPDs and B) all 64PPs determined in RHE exposed under different conditions. The dose of blue light was either 60 or 92 J.cm -² (BL60 or BL92, respectively). Results are median ± 25 th -75 th percentiles range. (Statistical significance of the difference with respect to pure UVB exposure: * p< 0.05; ** p< 0.01).

Figure 2 .

 2 Figure 2. Improvement of the repair efficiency (% repair) of TT CPD or all CPDs in the presence of photoprotectors during the BL exposure. A) unprotected compared to TriAsorb-protected RHE; B)unprotected compared to complete formula-protected RHE. Reported statistical significance of the differences was obtained by comparison with sample to BL 60 J.cm -2 without photoprotection and then UVB. Data, expressed in %, are median ± 25 th -75 th percentiles range. Results were obtained from 3 biological replicates involving 3 or 4 technical replicates (statistical significance between photoprotected and control RHE: * p< 0.05; ** p< 0.01).

Table 1 :

 1 Level of photoproducts (dimer per 10 6 normal bases)*. The dose of blue light was either 60 or

	92 J.cm -² (BL60 or BL92, respectively). Results were obtained from 6 to 3 biological replicates involving
	3 or 4 technical replicates.
	dimer	UVB t0	UVB t48h	BL60+UVB t0	BL60+UVB t48h	BL92+UVB t0	BL92+UVB t48h
	TT CPD	84.1±31.8 47.1±24.4*** 74.1±17.4	67.2±18.8	94.4±39.6	73.3±48.1
	TT 64PP	5.7±2.5	0.3±0.3***	6.0±1.5	1.1±1.2**	6.6±2.7	0.9±1.0***
	TC CPD	37.9±17.2	22.3±9.0***	39.5±8.6	35.0±11.3	42.8±23.8	38.0±21.1
	TC 64PP	35.1±16.8	1.7±2.2***	40.3±18.1	5.5±7.9**	36.2±32.0	3.8±5.3***
	CT CPD	12.2±8.9	4.0±4.1***	13.1±11.0	8.8±7.5	10.9±10.7	6.4±6.9
	* Data are median ± 25th-75th percentiles range. (Statistical significance of the difference between t0
	and t48h: ** p<0.01, *** p<0.001)

Table 2 :

 2 Repair efficiency (%repair)* for the different exposure protocols. The dose of blue light was either

	60 or 92 J.cm -² (BL60 or BL92, respectively). Statistical significance of the differences was obtained by
	comparison with pure UVB.
	dimer	UVB	BL60+UVB	BL92+UVB
	TT CPD	42.0±28.0	18.6±29.1*	7.9±71.1*
	TT 64PP	94.4±5.6	82.0±19.9*	84.6±16.5***
	TC CPD	42.4±23.4	16.4±26.8*	7.7±51.2**
	TC 64PP	94.9±6.7	84.0±23.1*	88.8±15.9*
	CT CPD	68.6±31.8	36.7±54.6**	49.8±53.4*
	* Data, expressed in %, are median ± 25th-75th percentiles range. Results were obtained from 6 to 3
	biological replicates involving 3 or 4 technical replicates. (Statistical significance of the difference with
	respect to pure UVB exposure: * p< 0.05; ** p< 0.01; *** p< 0.001).

DISCUSSION

The present results unambiguously demonstrate, for the first time, that BL hampers the repair of pyrimidine dimers in the DNA of reconstituted human skin tissue. This phenomenon was observed on CPDs, the repair rate of which was c.a. 50% in UVB-irradiated sampled and half of this value when a preliminary BL exposure was applied. Interestingly, a statistically significant effect was also obtained for 64PPs for which 95% of the damage was removed after 48h from UVB-irradiated RHE. These results provide additional evidence of possible deleterious effects of high energy visible light (400-450 nm) since the LED lamp used in this study was centered at 427±30 nm. In terms of underlying mechanism, the present observations are reminiscent of those made with UVA in a similar experimental design in primary cultures of human skin cells [START_REF] Courdavault | Repair of the three main types of bipyrimidine DNA photoproducts in human keratinocytes exposed to UVB and UVA radiations[END_REF][START_REF] Kimeswenger | UVA1 impairs the repair of UVB-induced DNA damage in normal human melanocytes[END_REF]. Explanation for this effect of UVA is likely associated with the capacity of these radiations at oxidizing and degrading DNA repair proteins [START_REF] Guven | Oxidative Damage to RPA Limits the Nucleotide Excision Repair Capacity of Human Cells[END_REF][START_REF] Montaner | Reactive oxygen-mediated damage to a human DNA replication and repair protein[END_REF][START_REF] Karran | Protein oxidation, UVA and human DNA repair[END_REF]. In this respect, we can speculate that BL could act as UVA by altering DNA repair process following protein oxidation. Further studies will be required to confirm this hypothesis. It may be added that no pyrimidine dimer could be detected by HPLC-MS/MS in the DNA of RHE exposed only to BL. This result is in agreement with our previous results in human skin [START_REF] Lawrence | The UV/visible radiation boundary region (385 -405 nm) damages skin cells and induces "dark" cyclobutane pyrimidine dimers in human skin in vivo[END_REF] but contrasts with that obtained with the less specific comet assay in cultured keratinocytes [START_REF] Chamayou-Robert | Blue light induces DNA damage in normal human skin keratinocytes[END_REF]. Other works in cell culture also failed at detecting CPDs at wavelengths higher than UVA [START_REF] Kielbassa | Wavelength dependence of oxidative DNA damage induced by UV and visible light[END_REF][START_REF] Kvam | Induction of oxidative DNA base damage in human skin cells by UV and near visible radiation[END_REF].

The other major result of the present study is that BL exposure of the skin model through a blue light absorbing/reflecting sunscreen specifically prevented decrease in repair capacities. It is now well established that sunscreens do prevent formation of DNA photoproducts, especially at high SFP. This was shown both in vivo [START_REF] Freeman | Sunscreen protection against UV-induced pyrimidine dimers in DNA of human skin in situ[END_REF][START_REF] Van Praag | Determination of the photoprotective efficacy of a topical sunscreen against UVB-induced DNA damage in human epidermis[END_REF][START_REF] Karbaschi | Rescue of cells from apoptosis increases DNA repair in UVB exposed cells: implications for the DNA damage response[END_REF], in RHE [START_REF] Bacqueville | Formulation of a new broad-spectrum UVB + UVA and blue light SPF50(+) sunscreen containing Phenylene Bis-Diphenyltriazine (TriAsorB), an innovative sun filter with unique optical properties[END_REF] and ex-vivo in skin explants (32-34,


Caroline Giroudon
email: caroline.giroudon@chu-lyon.fr

 Xavier Armoiry

 Maxime Fieux

Quality in systematic reviews: contribution of librarians Qualité en revue systématique : apport du documentaliste

Keywords: Problème, Intervention, Comparateur, Outcomes

Librarians play a crucial role in both the quantitative and qualitative aspects of health care research, given the establishment of a trusting relationship between them and the physicians leading clinical research. Well-executed systematic reviews contribute significantly to the practice of evidence-based medicine. This feedback presents a collaborative perspective involving a librarian and two clinicians regarding their joint efforts in completing eight systematic reviews. It delineates the assistance offered by the librarian and exemplifies how the clinicians' attitudes impact the service quality and, consequently, the credibility of these works.

 and selected Figure 2. MF and XA reviewed and modified the manuscript, Figure 1 and validated Figure 2.

Mots-clés

Résumé

Les documentalistes ont un rôle à jouer dans la démarche quantitative et qualitative de la recherche biomédicale, pour peu que s'établisse une relation de confiance entre eux et les chercheurs-praticiens. En effet, les revues systématiques (RS) de la littérature, bien conduites, peuvent appuyer la pratique de la médecine factuelle. Ce partage d'expérience est un regard croisé d'un documentaliste et de deux cliniciens hospitaliers sur leur collaboration dans la réalisation de huit RS. Il détaille le soutien apporté par le documentaliste et illustre combien la posture des cliniciens influence la qualité du service rendu, et par conséquent la crédibilité qui découle de ces travaux.

INTRODUCTION AND METHODOLOGY: CROSSED VIEWPOINTS OF A LIBRARIAN AND CLINICIAN

"Nothing has as much power to broaden the mind as the ability to examine systematically", said the philosopher emperor Marcus Aurelius. The practice of evidence-based medicine relies significantly on the utilization of the most current scientific data and knowledge pertaining to a given subject. In this context, systematic reviews (SR) of the literature can make a valuable contribution, provided they are conducted with the utmost rigor.

While recent literature has examined the qualitative contribution of librarians in conducting SR [START_REF] Schellinger | The effect of librarian involvement on the quality of systematic reviews in dental medicine[END_REF][START_REF] Rethlefsen | Librarian co-authors correlated with higher quality reported search strategies in general internal medicine systematic reviews[END_REF][START_REF] Meert | Impact of librarians on reporting of the literature searching component of pediatric systematic reviews[END_REF][START_REF] Koffel | Use of recommended search strategies in systematic reviews and the impact of librarian involvement: a cross-sectional survey of recent authors[END_REF][START_REF] Harris | The librarian's roles in the systematic review process: a case study[END_REF], few articles have synthetized the perspectives of librarians and clinicians regarding the necessity for collaboration in this demanding process. Nevertheless, this methodological feedback is crucial for supporting and advancing the involvement of librarians in these endeavors, ultimately contributing to the consolidation of evidence-based medicine [START_REF] Nicholson | Collaboration challenges in systematic reviews: a survey of health sciences librarians[END_REF][START_REF] Mckeown | Building capacity for librarian support and addressing collaboration challenges by formalizing library systematic review services[END_REF][START_REF] Obasola | Perceptions, experiences, and attitudes of health care professionals regarding the role of librarians in fostering evidence-based health practice: a systematic review protocol[END_REF].

With this objective, we aim to present our working methodology based on eight SR, either published or in progress, involving a documentalist and a clinician working in pairs within a French university hospital.

The initial segment of this article will elaborate on the support provided by the librarian to the clinicians, while the subsequent part will illustrate how the clinicians' engagement has influenced the quality of the service rendered by the librarian.

LIBRARIAN EXPERTISE TO SUPPORT RESEARCHERS

An escalating demand for SR support is becoming increasingly apparent in routine practice. This trend was identified in the literature by Cooper in 2013 as one of the future key points of the profession [START_REF] Cooper | New activities and changing roles of health sciences librarians: a systematic review, 1990-2012[END_REF]. In 2018, through a scoping review, the role of librarians was extensively delineated, and they were encouraged to articulate their involvement in this emerging activity [START_REF] Spencer | Roles for librarians in systematic reviews: a scoping review[END_REF]. Assisting in the creation of a SR necessitates librarians to possess a high level of expertise in documentary research, a substantial capacity for self-training, and proficiency in project management. Furthermore, dedicated time for the completion of a SR is imperative, given its time-intensive nature [START_REF] Campbell | What to Do When Everyone Wants You to Collaborate: Managing the Demand for Library Support in Systematic Review Searching[END_REF][START_REF] Borah | Analysis of the time and workers needed to conduct systematic reviews of medical interventions using data from the PROSPERO registry[END_REF]. The extent of time support provided is contingent on the trust vested in it by the practitioner and the proficiency levels of both parties. Certain clinicians solely request librarians to formulate research equations, while others engage them comprehensively in the project, spanning from conceptualization to publication (Figure 1).

In France, working with librarians for SR remains underdeveloped. However, akin to the increasing reliance on statisticians by researchers for meta-analysis, librarian assistance, particularly in the SR process, could evolve into an automated procedure and serve as a hallmark of good practice. According to the PRISMA (Preferred Reporting Items for Systematic Reviews and Meta-Analyses) recommendations, the formulation of an optimal search strategy constitutes a pivotal element in any SR [START_REF] Liberati | The PRISMA statement for reporting systematic reviews and meta-analyses of studies that evaluate healthcare interventions: explanation and elaboration[END_REF]. In this context, a section in the Cochrane Handbook for Systematic Reviews of Interventions (4.2.1), an international reference work, underscores the significant role assigned to literature search professionals [START_REF] Cumpston | Updated guidance for trusted systematic reviews: a new edition of the Cochrane Handbook for Systematic Reviews of Interventions[END_REF].

The crafting of the research strategy stands as the primary reason why practitioners seek the expertise of librarians. It serves as the equilibrium point in SR and necessitates joint validation with the practitioner based on a protocol. Similar to any experimental approach, this protocol allows the pre-establishment of scientific objectives and the methodology of the work. The protocol's significance lies in its description of the SR process. For transparency, we advocate for its publication in the Prospero international registration database [START_REF] Booth | The nuts and bolts of PROSPERO: an international prospective register of systematic reviews[END_REF]. Without robust search algorithms founded on PICO criteria (Population/Problem, Intervention, Comparator, Outcomes), systematic retrieval of available scientific evidence is unattainable. Librarians possess expertise in the specific language required for formulating search equations and are adept at combining controlled vocabulary (such as descriptors in a thesaurus, e.g., Mesh) with natural language. They proficiently employ Boolean operators (AND, OR, NOT, etc.), truncation, and limits to refine results. Their proficiency extends to recommending which databases (DB) should be queried, comprehending intricacies, and translating equations between DB (Pubmed, Web of Science, Embase, Cochrane Library, Scopus, etc.). Librarians establish monitoring systems facilitating clinicians in conducting dynamic rather than static SR, presenting a significant advantage. Literature indicates that the average time for a new clinical trial to be incorporated into an SR is approximately 4/5 years [START_REF] Elliott | Living systematic reviews: an emerging opportunity to narrow the evidence-practice gap[END_REF][START_REF] Shojania | How quickly do systematic reviews go out of date? A survival analysis[END_REF], and future updates have the potential to reduce this timeframe. The role of the librarian in collaboration with practitioners at this stage is pivotal, given that practitioners typically receive limited training in these methodologies. For instance, many are unfamiliar with the distinction between Pubmed and Medline [START_REF] Nlm. Medline | How are they different[END_REF], leading them to occasionally confine their searches to Mesh without realizing they may overlook recent articles integrated into Pubmed. As with all SR work, search algorithms must exhibit transparency and reproducibility, underscoring the importance of their high quality.

Once the research strategy is formulated, the librarian undertakes a task demanding rigor and methodology. They query databases, import results into bibliographic reference management software (EndNote, Zotero, etc.), and then perform the de-duplication phase, typically manually. Subsequently, they provide a file in RIS format, integrable by the clinician into bibliographic reference management software or a systematic review tool (Rayyan [START_REF] Ouzzani | Rayyan-a web and mobile app for systematic reviews[END_REF], Covidence, etc.). The two reviewers can then independently commence the initial "screening" phase (study selection) based on the title and abstract of the references. The second screening stage is then based on the full text of the references selected in phase 1. Here, the librarian locates and provides the full texts to the reviewers. This division of labor alleviates the clinician from conducting all the described steps, thereby optimizing medical time.

In the final phase of SR, some practitioners seek the librarian's assistance, as they can contribute to refining the search strategy, drafting the Prisma Flow Diagram [START_REF] Prisma | Prisma Flow Diagram[END_REF], or controlling the bibliographic references of the impending publication. In case of rejection following initial submission, the librarian can propose alternative journals leveraging their knowledge of scientific publishers and bibliometrics. However, the involvement of the information specialist should not be confined to the concluding phase, as the absence of a robust documentary search strategy from the outset may lead to "irrecoverable" methodological limitations, necessitating the initiation of the work anew.

Over time, librarians will enhance their skills and confidence, enabling them to support future professionals and residents embarking on SR, even those new to the methodology (Figure 2). They will guide them through various stages and offer advice on checks to be conducted in Prospero before commencing an SR.

PRACTITIONERS INFLUENCE THE QUALITY OF THE SERVICE PROVIDED BY THE LIBRARIAN

In this context, we draw upon the experiences of two university hospital practitioners, one of whom spent three years in an English university team specializing in secondary research. The findings demonstrate that clinician involvement has a profound impact on the librarian's work, influencing the quality of the human relationship established, the time dedicated to collaboration, and the effectiveness of methodological knowledge transfer. Supporting SR can be daunting for both seasoned and novice librarians [START_REF] Mckeown | Building capacity for librarian support and addressing collaboration challenges by formalizing library systematic review services[END_REF]. It is crucial for practitioners to be cognizant of this fact and adept at articulating their research objectives, blending technical expertise with accessibility. Similarly, the librarian's level of expertise in documentary research can be perplexing for practitioners whose proficiency in this domain may be rudimentary [START_REF] Moore | Teaching physicians to make informed decisions in the face of uncertainty: librarians and informaticians on the health care team[END_REF].

Librarians need two levels of understanding: that of the patient, to understand what they are looking for, and that of the practitioner, to search as closely as possible to the clinician's speciality. Once a relationship of trust has been established, everyone will be able to share their knowledge and skills for the benefit of the SR process. Time for exchange is precious and essential in terms of efficiency and quality. As much time as necessary, but as little as possible, is the subtle balance that the librarian must try to strike with the clinicians' workload. However, experience has convinced us that this time is unavoidable, particularly when it comes to detailing the parameters of the SR: eligibility criteria, chosen DBs, etc. The clinician must invest time in providing the essential information [START_REF] Mckeown | Building capacity for librarian support and addressing collaboration challenges by formalizing library systematic review services[END_REF][START_REF] Campbell | What to Do When Everyone Wants You to Collaborate: Managing the Demand for Library Support in Systematic Review Searching[END_REF]. Written exchanges of any kind are no substitute for direct communication. In order to optimise it, it should be prepared and supported by a written document, if possible the protocol or, failing that, the synopsis of the project. It is worth remembering that exchanges with a librarian are confidential.

In this article, we share a collaborative working experience that proves to be mutually beneficial for both participants: the librarian, well-versed in utilizing a thesaurus, formulates a Mesh-based equation. Subsequently, the librarian and clinician engage in discussions to amalgamate their dual expertise, encompassing both methodological and thematic aspects. The ensuing search algorithm is meticulously developed, leveraging the full range of possibilities offered by the thesaurus, whether in an exploded or nonexploded Mesh format. This collaborative ethos underscores that if clinicians can effectively impart their expertise with sufficient precision, the librarian's requirement for dual skills in documentation and medicine becomes discretionary.

The interpersonal dynamics and the allocated time significantly impact the quality of the service provided, with the clinician's teaching proficiency and methodological knowledge also playing crucial roles. The quality of this multidisciplinary exchange proves invaluable for both participants. Interprofessional training supplements self-training and the resources available to clinicians, such as Rayyan, among others. While systematic review training is readily accessible for librarians in the United States [START_REF] Mckeown | Building capacity for librarian support and addressing collaboration challenges by formalizing library systematic review services[END_REF][START_REF] Campbell | What to Do When Everyone Wants You to Collaborate: Managing the Demand for Library Support in Systematic Review Searching[END_REF][START_REF] Folb | Continuing education for systematic reviews: a prospective longitudinal assessment of a workshop for librarians[END_REF], its development in France remains limited. In 2020, Folb's study indicated that librarian participation in continuing education workshops on systematic reviews increased their knowledge levels and enhanced their skills [START_REF] Folb | Continuing education for systematic reviews: a prospective longitudinal assessment of a workshop for librarians[END_REF].

CONCLUSION: LIBRARIANS HAVE A ROLE TO PLAY IN THE QUANTITATIVE AND QUALITATIVE APPROACH TO BIOMEDICAL RESEARCH

This feedback demonstrates that the transfer of expertise from clinicians to librarians has proven to be a tangible asset. This transfer not only enables librarians to enhance their support capabilities for other researchers but also provides them with a form of scientific and methodological legitimacy. Librarians play a crucial role in the qualitative approach to biomedical research: they act as custodians of the reliability of the research equation, contribute to bias limitation, and, ultimately, can enhance the credibility of evidencebased research, thereby better supporting the practice of evidence-based medicine [START_REF] Kirtley | Increasing value and reducing waste in biomedical research: librarians are listening and are part of the answer[END_REF].

Adherence to the chronological process of a systematic review (SR) is fundamental. It is a systematic and organized procedure that necessitates a foundation in solid, reproducible research and specific skills. The inclusion of a librarian among the authors or in the acknowledgments is now considered a judgment criterion during the review phase and could potentially evolve into a future requirement. These two successive posts enabled her to develop her skills in a wide range of fields: medical, paramedical, administrative, professional and student. The first systematic reviews (SR) in which she participated in September 2016 dealt with stent-retriever thrombectomy for acute ischaemic stroke; they gave rise to two publications in 2018. When she was set up in 2017, she joined the Researchers' Team, a specialist team at Documentation Centrale, whose aim is to respond to the growing demand for SR and bibliometric information from physicians. She is dedicated to elevating the status of the documentation profession, while underscoring the significance of acquiring new skills to align with the evolving nature of the profession.

Xavier Armoiry has been a professor in pharmacy in Lyon since 2018. He divides his time between clinics at Hôpital Édouard Herriot, teaching and research at Université Claude Bernard Lyon 1. He is a specialist in health technology assessment, particularly medical devices, with a particular focus on clinical and medico-economic evaluation.

Maxime Fieux has been a clinical fellow in Professor Stéphane Tringali's O-HNS department since 2019. He aims to strengthen the HCL's regional and national influence in rhinology via the national collaborations he has developed through his involvement in the French Rhinology Association (AFR), of whom he is a member. With a passion for fundamental research, he has completed a Masters 2 in biostatistics and is currently working on his PhD thesis at the Paris Est Créteil university. He is working on biologics in chronic rhinosinusitis with nasal polyps and non-invasive routes of administration thanks to a transdisciplinary collaboration with the Verrier/Monge team at the LBTI, IBCP, Lyon, France. He is also been a teacher at the Lyon Sud Charles Mérieux Faculty of Medicine and Maieutics since 2019, where he teaches anatomy and ENT according to the programme defined by the French College of ENT and Cervico-facial Surgery, of whom he is a member.

FIGURE 1 :FIGURE 2 :

 12 FIGURE 1 : PROPOSED CHRONOLOGICAL SEQUENCE FOR CARRYING OUT A SYSTEMATIC REVIEW IN COLLABORATION WITH A LIBRARIAN AND TWO CLINICIANS


Benjamin Desrousseaux

Maarten Konings

Jérôme Loreau

François Lique

HD-H + collisions: statistical and quantum state-to-state studies

In the early Universe, the cooling mechanisms of the gas significantly rely on the HD abundance and excitation conditions. A proper modeling of its formation and destruction paths as well as its excitation by both radiative and collisional processes is then required to accurately describe the cooling mechanisms of the pristine gas. In such media, ion-molecule reactions are dominant. Their theoretical study is challenging and state-of-the-art quantum time-independent methods are computationally limited to collisions involving light molecules. Here, we report a state-to-state scattering study of the HD-H + collisional system using two different methods: an exact quantum time-independent approach and a recently developed fast and efficient statistical method. Reactive and inelastic rate coefficients were obtained for temperatures up to 300 K. The statistical method is able to reproduce exact calculations with an accuracy reaching the astrophysical needs while drastically reducing the computational resources requirements. Such results suggest that this new statistical method should be considered to provide the astrophysical community collisional data for which quantum calculations are impossible.

Introduction

In the Universe, hydrogen is the most abundant element and its molecular form, H 2 , constitutes the dominant molecule in astrophysical environments. It is now well established that H 2 and its isotopic variant HD are key species for the early Universe chemistry [1][2][3][4][5][6][7][8][9] and the cooling mechanisms of the low metallicity clouds and during the formation of the very first stars [10][11][12] .

The chemical composition of the primordial gas mainly consists of ionized species (e -, H, H + , H -, D, D + , He, He + , He 2+ , Li, Li + , Li -, H 2 , H + 2 , HD, HD + , HeH + , LiH, LiH + , H + 3 , and H 2 D + ), and ion-molecule reactions are known to be the dominant processes in the early Universe chemistry 2 . Due to their inherent practical advantages for preparation, control and detection, ion-molecule collisions have been subject to many experimental studies over the years 13 . However, the long-range attractive potential of these reactions and the common absence of large activation barriers make the theoretical studies challenging.

Quantum time-dependent or approximate semi-classical calculations struggle to reach the accuracy needed for astrophysical applications at low temperatures. Quantum time-independent treatment is therefore the method of choice to study collisions at typical astrophysical temperatures 14 . Still, this method requires extremely large amounts of computational resources and is currently limited to reactive systems with a low number of a Univ Rennes, CNRS, IPR (Institut de Physique de Rennes) -UMR 6251, F-35000 Rennes, France. E-mail: benjamin.desrousseaux@univ-rennes1.fr b KU Leuven, Department of Chemistry, Celestijnenlaan 200F, B-3001 Leuven, Belgium.

degrees of freedom and light collisional partners. As an alternative, a wide variety of statistical methods was developed to study chemical reactions and inelastic collisions (see for example the seminal work of Pechukas et al. 15 , Miller 16 , Quack and Troe 17 , 18 , Troe 19 ). Among them, the recently developed approach of Loreau et al. 20 , 21 inspired by the simple statistical adiabatic channel model (SACM) 17,18 , seems to offer a great alternative for the study of ion-molecule scattering. While overcoming the computational obstacles, this new statistical approach is believed to produce results that are sufficiently accurate for astrophysical applications and therefore needs to be benchmarked on relatively simple reactive systems, for which quantum-time independent calculations are feasible. Technical details on this improved SACM can be found in Refs 21,22 The H + + H 2 prototypical collisions have been extensively studied over many years. Indeed, the relative simplicity of the H + -H 2 collisional system and its isotopic variants represents a serious advantage for theoretical studies 23 . While the isotopic reaction D + + H 2 → HD + H + has been intensively studied, both experimentally [24][25][START_REF] Gerlich | Symposium on Atomic and Surface Phys[END_REF] and theoretically [START_REF] González-Lezana | [END_REF][28][29][30][31][32][33] , only a few data is available for the reverse reaction HD + H + → D + + H 2 24,[34][35][36][37][38] .

The HD + H + → D + + H 2 reaction is slightly endothermic by ∼ 320 cm -1 for the HD molecule in its ground rovibrational level but proceeds without activation barrier and becomes exothermic for HD in rotational states j ≥ 3. In the early Universe, the destruction of HD molecules through collisions with H + atoms is known to be effective as the temperatures generally allow overcoming the activation barrier of the reaction but also because HD ACCEPTED MANUSCRIPT rotational levels higher than j = 3 are found to be significantly populated. Moreover, the collisional excitation of HD plays an important role in the cooling mechanism of pristine gas where H + ions are present and even dominant colliders. It is then crucial to obtain accurate HD-H + collisional data for both the excitation and reactive processes.

Lepers et al. 37,38 recently reported exact quantum timeindependent close-coupling (CC) calculations of the state-to-state rate coefficients for the HD-H + collisional system. In this work, however, they only focused on the reactive process, providing no rate coefficients for the excitation of HD through collisions with H + whereas such data are also very useful for astrophysical applications 14 .

In this paper, we present a new theoretical state-to-state scattering study of the HD-H + collisional system where the calculations we carried out using two different methods: an exact quantum (CC) approach and a recently developed statistical method. Our goal was to provide new collisional data for this system, and (ii) to evaluate the accuracy of the SACM approach when studying reactive systems. A description of the methods can be found in Section 2. Results from both sets of calculations are presented and compared in Section 3. Concluding remarks and discussions are drawn in Section 4

Methods

During collisions between HD and H + , the inelastic (1), exchange (2), and reactive (3) processes compete:

HD(v, j) + H + → HD(v , j ) + H + (1)
HD(v, j)

+ H + → H D(v , j ) + H + (2)
HD(v, j)

+ H + → D + + HH (v , j ) (3)
where v and j denotes the vibrational and rotational level of the diatomic molecules. In our study of the scattering dynamics, this competition is taken into account and all three processes are considered. The VLABP H + 3 global potential energy surface (PES) of Velilla et al. 39 , properly describing the interaction energy in the reactants and reaction products channels, was employed in both our CC and statistical calculations. This PES represents an improvement of the long-range interactions from the ARTSM PES of Aguado et al. 40 , computed at the full configuration interaction (FCI) ab initio level and using an extended basis set. Figure 1 shows the HD-H + VLABP PES as a function of the Jacobi coordinates R and θ for a fixed internuclear r HD distance of 1.442 bohr, corresponding to the equilibrium distance of the ground vibrational state. In the Jacobi coordinate system, the centre of coordinates is placed in the HD centre of mass, and the vector R connects the HD centre of mass with the H + proton. The rotation of HD molecule is defined by the θ angle (θ = 0 • corresponds to the H + ••D-H configuration). As could be inferred from previous study on the H + + H 2 system (see Rao et al. 41 ), the VLABP PES is attractive for near T-shaped geometries while a barrier of almost 25 cm -1 is present for collinear geometries. The minimum configuration corresponds to θ = 100 • with a well depth of ∼35,600 cm -1 . In the following, the vibrational level of the molecules is omitted as we considered here low collisional energies implying that HD and H 2 remain in their ground vibrational level.

Close Coupling (CC) calculations

We used the ABC quantum reactive scattering program 42 to carry out CC calculations of reactive, exchange, and inelastic cross sections of the HD-H + collisional system. It is computationally efficient to choose basis functions that are eigenfunctions of the operator corresponding to interchange of the two hydrogens. Hence, since the Hamiltonian is symmetric with respect to interchange of the two hydrogens, there will be no coupling between odd (ortho) and even (para) rotational states of H 2 , so that the number of coupled channels is reduced. We then obtained inelastic, reactive and exchange integral cross sections following the approach described by Tao and Alexander 43 and recently used to study the rotational excitation of several hydrides in collision with H [44][45][46][47] . Excited vibrational states up to v = 17 and up to j = 6 (E max = 4.4 eV) are included in the basis to ensure convergence of the cross sections. The log-derivative method of Manolopoulos 48 was used to solve the coupled equations for hyperradii up to ρ max = 44 a 0 . Calculations were done for all values of the total angular momentum J leading to a non-zero contribution in the cross sections (∼60 at 1500 cm -1 , the highest considered energy).

Such calculations are in principle very similar to those performed by Lepers et al. 37 , 38 . However, the comparison between our results and those of Lepers et al. 37 , 38 shows a systematic difference in the reactive rate coefficients of a factor of ∼ 2. This systematic difference arises from the consideration of the two H atoms as either distinguishable or indistinguishable particles 49 . In this work, the two H atoms were considered as distinguishable particles as can be seen in Equations 1, 2, and 3.

Statistical approach

We used a new quantum statistical method inspired by the statistical adiabatic channel model (SACM) of Quack and Troe 17,18 .

2 | 1-7

ACCEPTED MANUSCRIPT

This method, described for the first time by Loreau et al. 21 , was successfully benchmarked on inelastic collisions involving several strongly-bound non-reactive systems (OH + -H, OH + -He, and CN --H 2 ), showing a very good agreement with CC calculations at low temperatures.

While for CC calculations the set of coupled differential radial equations:

- h2 2µ d 2 χ α dR 2 + ∑ α α H int +V + L 2 2µR 2 α χ α = Eχ α (4)
has to be solved for a given energy E and each value of the total angular momentum J, the so-called adiabatic curves of the reactants and reaction products channels are alternatively (there is no coupling between the different arrangements) obtained by excluding the nuclear kinetic term and diagonalizing only the W coupling matrix:

α H int +V + L 2 2µR 2 α ( 5
)
where µ is the reduced mass of the system, R is the distance between the center of mass of the molecule and the atom, and L is the angular momentum describing the relative motion of the two colliding partners. H int is the Hamiltonian describing the internal rotational motion of the molecule, V denotes the potential energy surface of the system, and |α corresponds to the angular basis set.

In our case, the molecules were considered as rigid rotors. We fixed the internuclear distances of the molecules at 1.401 and 1.442 a 0 for HD and H 2 , respectively. We used the molecular constants B e = 45.655 cm -1 , α e = 1.986 cm -1 and D e = 0.0260 cm -1 for the HD molecule, and B e = 60.853 cm -1 , α e = 3.062 cm -1 and D e = 0.0471 cm -1 for the H 2 molecule [START_REF] Herzberg | Molecular Spectra and Molecular Structure[END_REF] . For both molecules, rotational states up to j = 20 were considered. From the generated adiabatic curves, we construct the S matrix by assuming that all energetically open adiabatic channels (adiabatic curve for a given state) have the same probability:

S αβ (E, J) 2 =    1 N(E,J) for open channels 0 for closed channels (6)
where α and β represent the initial and final rotational levels of the molecule (HD or H 2 ) and N(E, J) is the total number of open channels for a given collision energy E and total angular momentum J. All open adiabatic channels at a given energy are included in the calculations so that the S matrix is converged with respect to the rotational basis. In our calculations, the ortho and para rotational states of the H 2 molecule were treated separately, meaning that ortho-H 2 channels were not taken in account when considering para-H 2 as a product of the reaction and vice versa. Given this separate treatment, one has to divide the reactive S elements by a factor of two, thereby conserving both symmetry and unitarity properties of the S matrix. The cross sections were then obtained from the constructed S matrix as: where g α is the degeneracy of the considered α state and k = √ 2µE.

σ α→β = π g α k 2 ∞ ∑ J=0 (2J + 1) S αβ (E, J) 2 (7)

Rate coefficients

The determination of the temperature-dependent rate coefficients was achieved by averaging the cross sections σ α→β over the collisional energy E:

k α→β (T ) = 8 π µk 3 B T 3 1 2 × ∞ 0 σ α→β Ee -Ec k B T dE, (8)
Where k B is the Boltzmann constant. For both methods, collisional energies up to 1500 cm -1 were explored in order to allow the determination of rate coefficients for collisions between HD in its first 6 rotational levels (0 ≤ j ≤ 5) and H + for, temperatures up to 300 K.

Results

Figure 2 displays the temperature variation of the rate coefficients obtained using pure CC approach for the inelastic, exchange and reactive processes for collisions of HD( j = 0) with H + , summed over all the possible final rotational states. As can be seen, exchange and inelastic rate coefficients are very similar in magnitude over all the temperature range explored in this work, reflecting the large well depth (∼ 35, 600 cm -1 ) in the PES and the statistical character of the reaction. The reactive process is negligible at very low temperature and only starts to compete with the excitation of the HD molecule for temperatures higher than ∼150 K, where the reactive rate coefficients become less than an order of magnitude lower than exchange and inelastic ones. This behavior is explained by the endothermicity of the HD + H + → H 2 + D + reaction (∼ 320 cm -1 ), resulting in reactive channels only opening at relatively high collisional energy.

From the astrophysical point of view, excitation through inelastic or exchange process cannot be distinguished. Hence, in the following, inelastic and exchange cross sections have been summed before computing the rate coefficients, denoted in the following excitation rate coefficients. It is also worth mentioning that, because of its intrinsic nature, the method used in this work assumes the same rate coefficients for the exchange and inelastic processes (see Refs. 21,22 ).

In Figure 3, we show the temperature variation of the rate coefficients for the rotational (de)excitation of HD( j = 0) → HD( j ) and HD( j = 1) → HD( j ) induced by collisions with H + . Results obtained using the CC method and the SACM are presented. The strongest transitions are those with ∆ j = 1, the magnitude of the rate coefficients increasing with decreasing ∆ j. Rate coefficients for the collisional excitation ( j < j ) of HD by H + are increasing with the temperature. For collisional (de)excitation ( j > j ), after a rapid increase, rate coefficients are slowly decreasing with increasing temperature. As can be seen, the two sets of data, obtained using whether the CC method or the SACM, are globally in very good agreement, with differences lower than a factor of 2.

A more systematic comparison of the two sets of data is presented 4 Systematic comparison between rate coefficients (in units of cm 3 s -1 ) obtained using the CC method and the SACM for the rotational excitation HD induced by collisions H + . Rotational transitions between the first 6 levels of HD are taken into account at three different temperatures: 50, 150 and 300K. The dashed lines delimit the region where the rate coefficients differ by less than a factor of 2.

ing the CC method for three different temperatures: 50, 150 and 300 K. All the possible transitions between the 6 first rotational levels of HD (0 ≤ j ≤ 5) are included in the comparison. As one can see, the agreement is very good, better than a factor of 2 at all presented temperatures and for all the transitions. These results demonstrate the ability of the computationally efficient SACM to properly describe state-to-state rate coefficients for the collisional excitation of the HD-H + reactive system.

We then focus on the reactive process of the HD-H + collisions. In Figure 5, we present the temperature dependence of the rate coefficients for the HD( j) + H + → H 2 + D + reaction, summed over all the final rotational states of the H 2 molecule. As expected, rate coefficients increase with increasing temperature. Rate coefficients for collisions involving higher initial rotational levels of the HD molecule are the largest in magnitude. The agreement between reactive rate coefficients obtained using the two different methods is again very good, the differences being of less than 30% and even almost zero for the reaction involving HD in its ground rotational level.

In order to further investigate the accuracy of the SACM at the state-to-state level, we present in Figure 6 a systematic comparison between state-to-state rate coefficients obtained using the CC method and the ones obtained using the SACM for the HD( j) + H + → H 2 ( j ) + D + reaction. Transitions between the first 6 rotational states of HD and H 2 are taken into account at three different temperatures: 50, 150 and 300K. As can be seen, the SACM is able to reproduce CC calculations to better than a factor of 2 for all the transitions and all represented temperatures, the maximum difference between the two sets of rate coefficients being of ∼ 40%.

Finally, we show in Figure 7 the thermal rate coefficient k th as a function of the temperature for the HD +H + → H 2 + D + reaction. The thermal rate coefficient was obtained assuming a Maxwell-Boltzmann distribution of the rotational levels of the HD molecule:

k th (T ) = 1 Z rot 5 ∑ j=0 (2 j + 1)e -E j k B T 9 ∑ j =0 k j→ j (T ) (9)
where E j is the energy of the HD( j) rotational level and

Z rot = ∑ 5 j=0 (2 j + 1)e -E j k B T
is the rotational partition function. We restricted the summations over the HD rotational level to j = 5 as higher levels are very weakly populated at the temperatures explored in this work and will not significantly affect the final result.

It should be noted that in order to compare to experimental results, one may take into account the nuclear-spin statistics for the two identical nuclei 49 . This is achieved by applying multiplying factors of 1 2 and 3 2 to rate coefficients corresponding to para and ortho states of the H 2 molecule, respectively:

k th (T ) = 1 Z rot 5 ∑ j=0 (2 j +1)e -E j k B T 8 ∑ j =0,2,... 1 2 k j→ j (T ) + 9 ∑ j =1,3,... 3 2 k j→ j (T ) (10
) However, applying such multiplying factors in the present case has no noticeable effect over all the temperature range explored Figure 7 so that using Equation 9 or 10 will give very similar results with differences of less than 2% at 205 K and less than 0.3% at 295 K).

As can be expected from the results presented above, thermal rate coefficients obtained using one or the other method are in very good agreement, the SACM only overestimating the rate coefficients by less than 20% over all the temperature range. Experimental results at 205 and 295 K from Henchman et al. 24 are also represented on Figure 7. Our theoretical results compare very well with the experiments, the CC thermal rate coefficient lying within the error bars at 205 K and being less than 30% larger at 305 K.

In this work, we presented statistical and close-coupling calculations for the scattering study of the HD-H + collisional system. From both methods, state-to-state excitation and reactive rate coefficients were obtained for temperatures up to 300 K. We showed that the SACM approach is able to reproduce CC results with a very good accuracy, the maximum differences being of less than 65% and 40% for the excitation and reactive processes, respectively.

We also computed the thermal rate coefficient for the HD + H + → D + + H 2 reaction and compared it to experimental results, which were available at 205 and 295 K. Our theoretical results are in very good agreement with experimental ones: At 205 K, the CC thermal rate coefficient is within the error bars and less than 30% higher than the experiments at 295 K. Again, the SACM gives very similar result, with less than 20% of differences compared to the CC thermal rate. Such findings strongly suggest that the the new HD-H + collisional data should be used for future applications.

It should be stressed that, because of its need in computational resources, CC calculations are very challenging to carry out for systems for which a large number of channels have to be considered. On the other hand, in the SACM approach, the diagonalization of the W coupling matrix is independent of the energy and the convergence of the cross sections with respect to the rovibrational basis is much faster than the convergence of CC cross sections: Unlike in the CC approach, it is indeed not necessary to include many closed channels in the ro-vibrational basis in the SACM as they will not account in the construction of the S matrix. While the present CC calculations for the HD-H + required a total of 470,000 CPU hours, the SACM was able to produce the rate coefficients using only 0.16 CPU hours. Hence, this new statistical approach should be considered as a great alternative to provide the astrophysical community collisional data for systems for which CC calculations are prohibitive nay impossible, such as interstellar reactive ions (H + 3 , H 2 O + , H 3 O + ) in collisions with H/H 2 .

Fig. 1

 1 Fig. 1 Contour plot of the HD-H + VLABP PES (in cm -1 ) as a function of the Jacobi coordinates for a fixed internuclear r HD distance of 1.442 bohr.

Fig. 2

 2 Fig.2Temperature variation of the rate coefficients for the inelastic, reactive, and exchange processes (summed over all final states) for colliof HD( j = 0) with H + .

Fig. 3

 3 Fig.3Temperature variation of the rate coefficients for the rotational (de)excitation of HD( j = 0) → HD( j ) (upper panel) and HD( j = 1) → HD( j ) (lower panel) induced by collisions with H + Solid and dashed lines represent results obtained using the CC method and the SACM, respectively.

Figure 4 .

 4 Fig.4 Systematic comparison between rate coefficients (in units of cm 3 s -1 ) obtained using the CC method and the SACM for the rotational excitation HD induced by collisions H + . Rotational transitions between the first 6 levels of HD are taken into account at three different temperatures: 50, 150 and 300K. The dashed lines delimit the region where the rate coefficients differ by less than a factor of 2.

Fig. 5 Fig. 6 Fig. 7

 567 Fig.5Temperature dependence of the HD( j) + H + → H 2 + D + reaction rate coefficients (summed over all the product rotational states). The solid and dashed lines correspond to results obtained using the CC method or the SACM, respectively.

| 1-7

| 1-7

Acknowledgements

This project has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (Grant agreement No. 811363). We acknowledge the Programme National Physique et Chimie du Milieu Interstellaire (PCMI) of CNRS/INSU with INC/INP co-funded by CEA and CNES. F.L. acknowledges financial support from the Institut Universitaire de France. J.L. knowledges support from Internal Funds KU Leuven through grant STG-19-00313. This work was granted access to the Occigen HPC resources of CINES under the allocation 2019 [A0070411036] made by GENCI.

Notes and references

Conflicts of interest

There are no conflicts to declare.


Jacques Saraydaryan

Fabrice Jumel

Olivier Simonin

Human Presence Probability Map (HPP): a Probability propagation based on Human Flow Grid

Personal assistance, delivery services, and crowd navigation through robots fleet are complex activities that involve human-robot interaction and fleet coordination. Human location estimation is one of the key factors in assisting robots in their tasks. This paper proposes an efficient process for propagating human presence probability based on partial observation of humans by the robot fleet. This process provides real-time information about the most probable region on the map where humans can be found. We propose a new problem representation allowing us to efficiently parallelize the propagation. To deal with the learned model and the real time robot observations, we propose to include a gaussian rotation probability process (VonMises [11]) combined with the previous learned observation to adapt the propagation. A set of experiments has been conduced with simulated environments that include real data allowing us to evaluate the model and to compare with the standard approach.

INTRODUCTION

Building robotic systems that can interact with humans remains a challenging task today. Knowledge about human behavior is crucial to develop humanacceptable and safe solutions. Navigating in populated environments or serving humans through robot fleets requires to understand human motion.

In this paper, we propose a scalable method to predict human motions in a closed environment from the observations colleted by a fleet of robots along the time. According to [START_REF] Rudenko | Human motion trajectory prediction: a survey[END_REF] our approach aims at computing human presence probability at middle term (> 10s). Indeed, middle term prediction is particularly important for robot fleet tasks achievements, where a robot could benefit of other robots observation to adapt its behavior and decision. In other words, we build a Human Presence Probability Map from robot observations. We build our approach over an existing discrete human orientation probability map [START_REF] Jumel | Mapping likelihood of encountering humans: application to path planning in crowded environment[END_REF], called Flow Grid Map, similar to [START_REF] Kucner | Probabilistic Mapping of Spatial Motion Patterns for Mobile Robots[END_REF][START_REF] Vintr | Spatio-temporal Representation of Time-varying Pedestrian Flows[END_REF]. Then we are able to propagate online human observation information which is exploited by robots to navigate efficiently and to find humans in order to serve them.

The figure 1 shows an example of Human presence probability propagation on an entire closed environment. Here, an existing flow grid is used to help the propagation. Each time a robot detects a human, the algorithm begins to propagate the information. The cumulative information through all robot observations results in a map highlighting the probability to meet pedestrian.

This paper is organized as follows: Section 2 describes related works in human flow modeling and human motion trajectory prediction. The section 3 explains Human flow grid models used as computation baseline. The section 4 describes our human presence probability propagation computation and associated optimizations. Finally, the section 5 shows experiments and results.

RELATED WORK

Human motion prediction get a growing interest recent years. Human motion prediction could be divided into two different objectives: short term prediction (1-2s) and long term prediction (up to 20s) [START_REF] Rudenko | Human motion trajectory prediction: a survey[END_REF]. Moreover Rudenko and al. [START_REF] Rudenko | Human motion trajectory prediction: a survey[END_REF] propose to distinguish different kind of modeling approaches. Physics-based modeling aims at simulating a set of explicitly defined dynamics equation that follow a physics-inspired model. Such methods predicts human motion after sensing the environment and are mostly used in short term prediction (e.g [START_REF] Kooij | Context-based path prediction for targets with switching dynamics[END_REF]). Planning based methods are more focused on long-term motion. After sensing the environment, hypothesis are used to estimate path used by human to reach their goals. Finally, Pattern-base methods intents to learn motion model after sensing the environment. This kind of methods (sequential methods) could learn conditional models over time and recursively apply learned transitional function for inference or model the distribution over full trajectories. In this paper we particularly focus on Pattern-based approaches and especially sequential methods. In such approaches conditional models are learned from observation and mainly used Markov models. Some works intends to model local transition such as probabilities of transition between cells on a grid map [START_REF] Jumel | Mapping likelihood of encountering humans: application to path planning in crowded environment[END_REF][START_REF] Mellado | Modelling and predicting rhythmic flow patterns in dynamic environments[END_REF][START_REF] Kucner | Enabling Flow Awareness for Mobile Robots in Partially Observable Environments[END_REF]. Other methods use Recurrent Neural Networks (RNN) or Long Short-term Memory (LSTM) to learn sequence of motions. Such recent methods gives good result especially on short therm prediction [START_REF] Xie | Towards safe navigation through crowded dynamic environments[END_REF], nevertheless lots of data is needed for training such network and computed models are sensitive to motion habits changes. Other interesting approaches compute clusters on observed trajectories to predict human motion [START_REF] Han | Pedestrian motion model using non-parametric trajectory clustering and discrete transition points[END_REF][START_REF] Zhou | Learning collective crowd behaviors with dynamic pedestrian-agents[END_REF]. Despite very good prediction results, these methods suffers of same limitation as RNN or LSTM approaches. Moreover, most these methods needs either a complete trajectory monitoring (e.g start and goal position of pedestrian) or a capacity to re-identify pedestrian. Such constraints do not fit our current hypotheses of partial pedestrian observation thought a robot fleet.

As presented in section 1, the human motion prediction can help robot to compute a better navigation (socially acceptable, reducing travel time) or increase the service to human. With partial human motion observation, we need to inform the robots about human motion with learned trend and with recent observation. Furthermore, the more the map used for navigation will be informed, the more the service to human efficiency will increase. Such information is precious to help the robots to navigate [START_REF] Fulgenzi | Probabilistic motion planning among moving obstacles following typical motion patterns[END_REF][START_REF] Saraydaryan | Navigation in Human Flows : Planning with Adaptive Motion Grid[END_REF]. This kind of hypotheses reduces the choose of modeling approaches. We choose to improve methods modeling transitions between cells with an efficient probability propagation process. We extends such methods [START_REF] Jumel | Mapping likelihood of encountering humans: application to path planning in crowded environment[END_REF][START_REF] Mellado | Modelling and predicting rhythmic flow patterns in dynamic environments[END_REF][START_REF] Kucner | Enabling Flow Awareness for Mobile Robots in Partially Observable Environments[END_REF] with the help of both learned trends and recent observation to deal with our context constraints.

Flow grid reminder

The authors in [START_REF] Jumel | Mapping likelihood of encountering humans: application to path planning in crowded environment[END_REF] defined a map reflecting the probability to meet a human with a certain direction. This map is computed as follows.

In each cell c x,y , we discretize the possible flow directions by a set of K directions, and we note k i ∈ K each direction 1 . For instance, we can set K = {N orth, N orthEast, ..., South}. We note Z t the set of observation performed by all the robots up to time t. An observation, in a cell c x,y , consists in identifying a human direction, eventually none, and its duration. By hypothesis, only one human can occupy a cell at a given time. In practice, we consider cell sizes from 0, 25m 2 to 1m 2 . Let note R = r 1 , r 2 , ..., r n the set of robots. We note t cx,y(r) the sum of the durations of all observation (human observed or not) performed by the robot r on cell c x,y . t c x,y,k (r) is the sum of durations of the observation of a human moving in direction k in cell c x,y . We set M f low = ∀x∀y∀k(M c x,y,k ) the grid of human motion likelihood in every direction k of each cell c x,y , called Flow grid. By considering that human flows are stationary processes, each cell value is computed (updated) as follows:

M c x,y,k (Z t ) = |R| n=1 t c x,y,k (r n ) |R| n=1 t cx,y (r n ) (1)
To deal with non stationary processes a forgetting factor could be added as is was done in [START_REF] Saraydaryan | Navigation in Human Flows : Planning with Adaptive Motion Grid[END_REF]. By extension, the probability to meet a pedestrian in a given cell is defined by:

M presc x,y (Z t ) = k∈K M c x,y,k (Z t ) (2)
The Flow grid could be extended if the probabilities is related to some hour of the day and day of a week as its was suggested in [START_REF] Vintr | Spatio-temporal Representation of Time-varying Pedestrian Flows[END_REF]. Thus, the likelihood to meet a human in a given orientation k is noted M t day cx,y,k where t day represents the likelihood at a given day/week time (e.g Monday 10h12).

4 Human Presence Probability Map (HPP Map) Once we are able to compute information about human flow, as it was explained in section 3, we have to provide a method to propagate pedestrian presence probability when these ones have been detected by robots.

To do so, we assume that this likelihood M cx,y,k gives us a transition probability between the current cell c x,y and the neighbor cell targeted by the given orientation

k. E.g if k means north, an current cell is c 1,1 , M c1,1,N orth ≡ P (c 1,1 - → c 0,1 ).
Without additional information finding the most likelihood human presence on a given direction could be expressed such as: argmax(M cx,y,k ). This information only takes into account human presence flow model and not recent/current human observation. In order to predict the human position in next seconds and more, we have to combine pre-computed human flow grid and current set of observation.

A common probability propagation could be expressed as follows: For each neighbor cells around the discrete observation z t

x,y,k θ , let note P t+1 pres (c x1,y1,k )

the probability to meet the previously observed human on the cell c x1,y1 at t + 1 with the orientation k.

P t+1 pres (c x1,y1,k |z t x0,y0,k θ ) = M cx 1 ,y 1 ,k ||K|| i=1 M cx 1 ,y 1 ,ki × α × P t pres (c x0,y0,kc |z t x0,y0,k θ ) (3)
where k c is the orientation pointing to the current cell c x1,y1 , k θ is the approximated orientation θ of the observation,

P t pres (c x0,y0,kc |z x0,y0,k t θ ) = 1 if k θ = k c , 0 otherwise and α ∈ [0; 1] represents a stationary coefficient.
The figure 2 illustrates this principle. On the left we find input data, the learnt flow grid and a robot observation. The probability propagation process is represented from t 0 to t 3 . On the bottom, the likelihood of pedestrian presence over the time is represented. Each blue arrow on each cell defines the probability to meet human in a given direction. The total probability to meet a human on each cell is represented on the top.

For a set of observation occurring at different times, noted Z 1:t , each cell accumulates the propagated probability of each observation:

P t pres (c x,y,k |Z 1:t ) = 1 ||Z 1:t || ||Z 1:t || i=1 P t pres (c x,y,k |z ti xi,yi,k θ i ) (4)
The resulted matrix representing the probability to meet human moving in a targeted direction is called Human Presence Probability Map (HPP Map) To make easier the parallelization of the computation, we propose to reformulate the problem as follows: On one side, at a time t, a cell get the sum of cumulative probability from a set of observation Z 1:t . On the other side, the cell contributes to the probability propagation to neighbors cells. We propose to formulate the probability of presence of a human in a given cell as follows:

Scalability and Propagation Optimization

P t pres (c x,y,k |Z 1:t ) = α × M c x,y,k ||K|| i=1 M c x,y,k i × ||N (cx,y)|| j=1 P t-1 pres (c xj ,yj , k c |Z 1:t ) + (1 -α) × P t-1 pres (c x,y,k |Z 1:t ) (5)
where ||N (c x,y )|| is the cardinality of neighbourhood of c x,y ,

||N (cx,y)|| j=1 P t-1 pres (c xi,yi , k c |Z 1:t )
represents the probability propagation of each neighbors cells and (1 -α) × P t-1 pres (c x,y,k |Z 1:t ) the previous cell value minus the current cell propagation effort to neighbor cells.

Such reformulation allows massive parallelization. At t each HPP Map cells could computes its t+1 value without waiting computation from neighbors. This property allows a GPU implementation of the HPP Map computation.

Moreover, some flow grid cell could be uninformed, meaning that no observation has been made in flowgrid map. In such situation, we assume that human motion follows a Gaussian orientation change model as described by Von Mises equation such as:

V onM ises(θ k , θ k ref ) = e Ccos(θ k -θ k ref ) 2πI0(C)
where 1 C = σ 2 and θ k and θ k ref represents the angle of a given orientation (e.g if K means North,

θ k = π
2 ) respectively for a given orientation and a referent orientation. I 0 is the modified Bessel function of order 0.

Thus, for uninformed flow grid cell, the probability propagation could be defined as:

P t+1 pres (c x1,y1,k |z t x0,y0,θ ) = V onM ises(θ k , θ kc ) × α × P t pres (c x0,y0,kc |z t x0,y0,k θ ) (6)
The figure 3.a shows an example of application.

The flowgrid maps give a trend of human motion. In some situation, some observation not fit computed model. E.g if an observation was made from a cell to a given direction, if the targeted cell contains high probabilities to go back to the current cell, the system would not take into account the characteristic of the current observation. To avoid such behavior, we propose to use again the Von Mises function to combine current observation motion and human motion trends. This approach will temper probability propagation by combining the current observation and the learnt flow grid map. The resulting value is expressed as follows:

P t+1 pres (c x1,y1,k |z t x0,y0,θ ) = V onM ises(θ k , θ kc ).M c x,y,k ||K|| i=1 M c x,y,k i × α × P t pres (c x0,y0,kc |z t x0,y0,k θ ) (7)
The figure 3 shows an example of propagation using such equation. In the figure 3.b situation only flow grid information is used to propagate probability. In such case half of probability is send back to the cell where the observation was made. Such behavior means that the human has 50 per cent to half turn. In the figure 3.c case, we apply Von Mises coefficients to prioritize ongoing moves, reflecting a more realistic propagation.

Experimentation

Fig. 4: Real ATC scenario. On the top, the original configuration scenario as mentioned in [START_REF] Brscic | Person tracking in large public spaces using 3-d range sensors[END_REF]. On the bottom, the scenario played with 3 robots following Hamiltonian path, flow grid learning and HPP computation Fig. 5: Museum Scenario (Artificial Scenario). On the top, the scenario map and the set of way points following by 2 pedestrian groups. On the bottom, the scenario played with 4 robots following Hamiltonian path, flow grid learning and HPP computation Our first series of experiments was made on a simulated environment using the ROS version of Pedsim simulator [START_REF]Ros packages for pedsim (pedestrian simulator) based on social force model of helbing et. al[END_REF]. This experiment involved 50 pedestrians walking through pre-defined trajectories (Figure 5). The environment is composed of several corridors and rooms. In this experiment case, we want to highlight the performance improvement of computing Human Presence Probability propagation with a standard implementation with python and numpy, and a GPU implementation using Numba [START_REF] Lam | Numba: A llvm-based python jit compiler[END_REF]. For experimentation, we use the flow grid described in our previous worked [START_REF] Jumel | Mapping likelihood of encountering humans: application to path planning in crowded environment[END_REF]. In this scenario, 4 robots allowing wide-ranging observations (360°field of view with a range of 3 meters ) navigate across the environment according Hamiltonian path [START_REF] Portugal | A survey on multi-robot patrolling algorithms[END_REF] (optimising the space coverage). Thus the robot fleet covers the environment and updates the human presence (z x,y,k t θ ) when a pedestrian is met (in the robot field of view). We assumed that probabilities coming on map walls are removed. This experiment was conducted during 800 seconds. The experiment was made on a laptop i7, 9th gen., 16Go RAM, graphic card NVIDIA Quatro T1000. With an average processing time of 1.632s (to propagate the HPP of the entire environment at each processing step) for the standard implementation and 0.052s for the GPU implementation, this gain of more than 30 times make the usage of the HPP map computing online realistic. During this scenario, most probable regions to meet people are clustered (HPP clusters) and human position ground truth is used to evaluate the distance between real human position and HPP clusters. In other words, the lower the average distance is, the more the pedestrian estimation is accurate. The figure 6.b shows the HPP Cluster centroids. To build such clusters, we first filter HPP Map (figure 6.a) data that are above a threshold. Here we assume that probabilities below such threshold are not sufficient to be representative of Human position estimation. A DBscan [START_REF] Schubert | Dbscan revisited, revisited: Why and how you should (still) use dbscan[END_REF] clustering algorithm is then applied and resulted cluster centroids are displayed by a colored cross in the figure 6.b). At the end, tracked pedestrian are affected to the closest cluster centroid (wave front propagation from the targeted cluster center) and distance between pedestrian position and cluster centroid is measured. The error measure could be expressed by error hi = arg min clust∈DBscan(HP P M ap) dist(clust, h i ) , where clust is a cluster centroid and h i the ground truth of a pedestrian pose. We compare our results obtained in such scenario with two other approaches:

one long term design approach: human affordance map [START_REF] Tipaldi | I want my coffee hot! Learning to find people under spatio-temporal constraints[END_REF] aims at building a statistical representation of human presence (only human presence per cell is considered in such approach). -one short term design approach: Kalman prediction, where humans are tracked through well known Kalman filter [START_REF] Kalman | Others: A new approach to linear filtering and prediction problems[END_REF].

The human affordance map uses robot observation to update the probability to meet human on each map cell during the time. The human affordance map is updated all experimentation long. As it is done for HPP map, at each evaluation step, a DBscan cluster algorithm distinguishes a set of most probable human presence area based on the human affordance map. Then each observed human is affected to the closest cluster. The distance between human and its associated cluster centroid is considered to evaluate the prediction precision (figure 6.c).

The Kalman prediction is also used to predict pedestrian pose. When robot meet a pedestrian, a Kalman filter is created and updated as long as the associated pedestrian is in the field of view of a robot. Otherwise the Kalman filter continue to predict the next pedestrian position. The distance between the pedestrian pose ground truth and the Kalman prediction is considered to evaluate the prediction precision (figure 6.d). All Kalman filter are set with the associated pedestrian pose, an acceleration of 0.68m.s 2 and an acceleration standard deviation of 0.2 based on recommendation of [START_REF] Teknomo | Microscopic pedestrian flow characteristics: Development of an image processing data collection and simulation model[END_REF]. The evaluation process was made as follows: pedestrian detected by robot are tracked (ground truth position) during different time range (from 10s to the end of experiment). For each tracked pedestrian, the distance between ground truth pose and associated prediction is measured for each evaluation process:

-HPP : Distance to the closed hpp cluster -Human affordance : Distance to the closed human affordance cluster -Kalman prediction : Distance to the associated Kalman filter prediction pose.

The results of the average distance of all ground truth pedestrian poses and HPP cluster centroids are available in the Figure 7.

In the Figure 7.a, the average distance is measure during the time. Each colors refers to different pedestrian track duration. For instance, the orange curve refers to a track during of 10s meaning that over 10s of a pedestrian tracking, this one is no more tracked and its ground truth position is forgotten. We can notice that the average distance decrease over the time. This observation is due to the enrichment of the flow grid map, increasing the accuracy of the HPP. In the figure 7.b the cumulative average distance is computed. It comes as no surprise that lower pedestrian tracking duration implies best pedestrian prediction. We can notice that tracking pedestrian during 30s (brown curve) or tracking over the whole experimentation (800s, blue curve) results of no significant difference compare to duration of 10s or 30s.

The results of the average distances (average of all ground truth pedestrian poses and cluster centroids/estimators) of each processes are available in the table 1. In this table, we compare two versions on HPP, one with the VonMises propagation model, and one without. The capacity of the VonMises propagation model to balance current pedestrian observation/direction and the learnt flow gives better results on all different pedestrian tracking duration. The HPP with VonMises get best results on all pedestrian tracking durations except for 800s duration. In this case, Human affordance coupled with the flow grid already learnt get better results. This can be explain by the fact that the more the tracking duration is the more the pedestrian as a chance to not being met by a robot and so the static statistical Human probability representation (human affordance map) get best results. We also highlight the influence of the flow grid, both learning flow grid from the start and previously learnt flow grid at the exprimentation start have been played. We can notice that concerning the Human affordance map or HPP Map results are significantly better when flow grid is already learnt. The second set of experiments was made on a subset of the ATC pedestrian tracking data set [START_REF] Brscic | Person tracking in large public spaces using 3-d range sensors[END_REF]. This dataset is the result of tracking people on an ATC shopping center in Japan over about 900m 2 between October 24, 2012 and November 29, 2013. We extract a subset of this dataset (data of the 2012/11/14). The interaction between robot's moves and the crowd is considered by integrating real data into the pedsim simulator:

-Extract consecutive series of individual pedestrian position -Sample individual pedestrian position -Convert samples pose into way points -Create pedestrian at the apparition time, following its associated way points Between way points, each pedestrian is driven by Pedsim local planner (repulsive and attractive potential forces) and thus avoid collision between other simulated pedestrian or robot. The same evaluation process used in the first experiment is applied. The results of the average distances (average of all ground truth pedestrian poses and cluster centroids/estimators) of each processes of the ATC scenario are available in the table 1.

The results show the same trends found the first experiment. HPP Map with VonMises get the best results no matter the pedestrian tracking duration. Results became also better when an already learnt flow grid is used. In this set of experiment, Human affordance process do not overcome the HPP Map method for long pedestrian tracking (e.g 800s). This result is mainly due to the fact that in the ATC dataset pedestrian appear and disappear on quite short period meaning that a tracking no more exceed 30s.

The experiments carried out are illustrated in the video here2 . Our proposition outperforms other tested models by an average of 17% (and up to 40% in certain conditions).

CONCLUSION

In this paper, we propose a new method for propagating human presence probability based on partial human observation by a robots fleet. With the help of a Flow grid Map, representing the probability to meet human in a cell in a direction, we propagate probabilities as soon as a robot observes a human. By reformulating the problem, we manage to massively parallelize computation (GPU) allowing online Human Presence Probability propagation. Thanks to the applied optimization (VonMises), our method is able to handle both learned trends and current observations. Our experimental results, conducted on two different scenarios (an artificial and a real-life dataset), demonstrate that our model outperforms existing long-term (Human Affordance Map) and short-term (Kalman estimator) human presence estimators.

Fig. 1 :

 1 Fig. 1: HPP Map representation on closed environment

Fig. 2 :

 2 Fig. 2: Example of human presence probability propagation

Fig. 3 :

 3 Fig. 3: Von Mises propagation optimisation: a) no information is held by the flow grid map, Von Misies coeffient are used to propagate, b) flow grid held information, propagation only used flow grid, c) both flow grid and Von Mises Coeff are used

Fig. 6 :

 6 Fig. 6: Pedestrian position prediction evaluation steps

Fig. 7 :

 7 Fig. 7: Average distance from ground truth and HPP clusters during the time. The figure a shows average distance from HHP cluster using a sliding windows of 20. The figure b represents the cumulative average error distance over the time.

Table 1 :

 1 .50 12.53 16.12 7.45 8.11 8.52 8.77 8.91 9.00 HPP With VonMises Flow grid learnt 3 5.38 6.01 6.81 7.87 8.79 13.02 4.29 4.95 5.44 5.49 5.53 5.81 Human affordance 13.46 13.86 14.01 14.04 13.96 12.99 14.63 15.06 15.84 16.44 16.55 16.55 .65 11.05 11.26 11.90 Kalman Prediction 13.01 14.83 16.582 18.05 19.11 24.01 11.69 13.67 15.21 16.16 16.57 16.63 Average distance (in meter) of pedestrian between computed pedestrian pose estimation and ground truth from Museum scenario (artificial scenario) and Real ATC dataset

				Museum Scenario					Real ATC scenario
	Tracking duration (in s.)	10	15	20	25	30	800	10	15	20	25	30	800
	HPP Without VonMises	10.60 12.57 13.96 14.96 15.66 21.31			Not Tested
	HPP With VonMises 10.20 11Human affordance Flow grid learnt 3 6.58 8.54 9.29 9.27 9.14 9.13	9.14	9.03	9.00	9.83 10

When a robot detects a human in x, y pose with θ orientation z x,y,θ , we approximate the orientation θ to a discrete orientation k.

https://youtu.be/H7Ly9nZKNks

For ATC Scenario 500000 records was used to learn the flow grid, the next 500000 records are used to evaluate the model