Jad Abou Chaaya
email: jad.abouchaaya@ieeee.org

Arnaud Coatanhay

Ali Mansour
email: mansour@ieeee.org

Thierry Marsault
email: thierry.marsault@intradef.gouv.fr

Joint Trajectory and Communication Optimization for UAV in Complex Electromagnetic Environment

Keywords: Unmanned Aerial Vehicle (UAV), Trajectory Optimization, Mixed Integer Linear Programming (MILP), Multiple Knife Edge (MKE) Diffraction, Path Loss (PL) Threshold Optimization

Unmanned Aerial Vehicle (UAV) is a booming trend in major civil and military applications such, but not limited to, transportation, delivery, and surveillance missions. In order to accomplish the mission's objective, trajectory planning must be optimally achieved. The communication link established between the UAV and the ground/aerial stations is the main factor to account for designing the trajectory. However, this link is highly affected by the shape of the topography, especially when the UAV must fly at a low altitude between mountains of variable elevations. Therefore, this paper addresses the challenge of three-dimensional trajectory optimization for low/mid-altitude flying UAVs in complex propagation environments. To tackle this challenge, we propose a system model for the trajectory using the diffraction phenomenon with Multiple Knife Edge (MKE) to model the channel between the UAV and the station when the Line of Sight (LoS) is absent. Then, we propose a joint optimization to minimize the trajectory and maximize the communication quality via the Mixed Integer Linear Programming (MILP) problem design and solution. We validate the proposed approach by using real terrain profiles in the simulations with a rough topography; where the LoS propagation aspect is barely present. Our approach is able to jointly find, when physically achievable, the UAV trajectory with the shortest path and the "best feasible" communication quality.

I. INTRODUCTION

Unmanned aerial vehicles (UAV) are expanding quickly and becoming a crucial component in basic technological systems, especially in telecommunication, wireless networks, and military fields [START_REF] Zeng | Energy-efficient uav communication with trajectory optimization[END_REF] [START_REF] Mozaffari | A tutorial on uavs for wireless networks: Applications, challenges, and open problems[END_REF]. The emergence of the beyond 5G architectures allows UAVs to be used as aerial base stations for coverage and capacity enhancement. In [START_REF] Zhang | Joint trajectory and power optimization for uav relay networks[END_REF], the UAV is used as an amplify and forward relay in the network; whereas in [START_REF] Lee | Trajectory planning for multiple uavs in uav-aided wireless relay network[END_REF] and [START_REF] Dat Nguyen | Trajectory control and resource allocation for uav-based networks with wireless backhauls[END_REF], it is used as a flying base station for covering wireless backhauls. The UAV plays a major role in the military context, especially for surveillance and operational missions. In all previously cited applications, the trajectory planning and optimization is very important for a successful mission accomplishment.

UAV navigation presents many constraints like flight time, energy consumption, dynamics, channel variation, propagation model, collision avoidance, flight altitude, and many more. Given the flight context, where the UAV should accomplish a sensitive mission with a specified task, the important aspect to consider is maintaining the communication link between the UAV and the command center. For sensitive applications, specifically the military, the trajectories may address nonclassical requirements such as the low-altitude flight behavior. These requirements severely penalize the Line of Sight (LoS) between the UAV and the communicating node present at the ground or in the air. The link becomes difficult to maintain and full of communication holes especially when the terrain presents rocky topography such as mountains, hills, and cliffs. The propagation of electromagnetic waves given such environments presents a challenging issue for radio and wireless communication systems, where the LoS is barely considerable and unrealistic to account for.

In the literature, for most of the UAV's trajectory planning, the classical adopted air-to-ground propagation channel models ( [START_REF] Khawaja | A survey of air-to-ground propagation channel modeling for unmanned aerial vehicles[END_REF], [START_REF] Al-Hourani | Modeling air-to-ground path loss for low altitude platforms in urban environments[END_REF], [START_REF] Al-Hourani | Optimal lap altitude for maximum coverage[END_REF]) consider the urban zones and use statistical properties to decompose the channel in a LoS and non-LoS components. Such models are inadequate and unrealistic to use in the case of the challenging complex propagation environment that creates plenty of communication dead zones (due to the continuous rocky elevations). To tackle this issue, we are interested in the Multi Knife Edge (MKE) diffraction phenomenon and precisely by the Vogler [START_REF] Vogler | An attenuation function for multiple knife-edge diffraction[END_REF] algorithm to compute it. We believe that in our case the diffraction model will significantly compensate for the terrain effect and explore the communication dead spots. As per our knowledge, no study in the literature adopts the diffraction phenomenon to model the channel between the UAV and the communication node. Therefore, in this paper, we consider the MKE diffraction to model the communication for the flying platform [START_REF] Nguyen | On the proof of recursive vogler algorithm for multiple knife-edge diffraction[END_REF], [START_REF] Nguyen | Deep learning based higher-order approximation for multiple knife edge diffraction[END_REF]. Hereinafter, we propose a system model for the UAV trajectory and derive a criteria to find the optimal path with respect to the distance and the communication quality. The main contributions of this work are listed as following:

• Proposing a system model for UAV trajectory planning given terrains with rough topography that presents a complex environment for the radio propagation. To overcome this challenge, the MKE diffraction between the station and the UAV is used to model the communication for Non-LoS (NLoS) situations, where some significant wave energy is gained thanks to this phenomenon. • Formulating the trajectory and the communication quality optimization using a weighted multi-objective cost function to allow a tradeoff between the shortest distance and a "best feasible" communication quality in terms of path loss. The problem is formulated using the MILP scheme and solved using commercial solvers. • Validation of the proposed system model, problem formulation, and optimization scheme using real terrain data with geographic 3D coordinates in the region of southern France at the border with Spain near the Pyrénées mountains.

II. SYSTEM MODEL

We explain the assumptions and the description of the UAV problem in II-A. Then, in section II-B, we explain the MKE diffraction. We formulate the communication model, in terms of path loss, between the UAV and the base stations in II-C.

A. Assumptions and Parameters Description

We consider a multi-purpose and long-endurance flying UAV. All possible locations for the UAV navigation during the mission time can be represented as infinity points in the 3D space. We sample this three-dimensional space to a limited number of points to produce the map in "Fig. 1". The location map consists of a predefined number of points, where each represents a position in the 3D space. The drone flies with a velocity of v(t) (m/s). The time flight is decomposed into a predefined number of time segments, where the duration of each slot is expressed in seconds. The starting position and the departure time of the UAV are selected by the user. To simplify the model and improve the operational efficiency, we assume that the UAV can fly only to one position per assigned time slot or it can hover at the same place. The spatial step of the drone is defined by its speed and the time slot duration. The arrival location of the drone is also defined by the user. The cartesian coordinate system for the three-dimensional space is adopted for modeling. However, for simulating the real terrain environment, the geographic coordinate system is used with latitude, longitude (in degrees), and elevation (in meters). We sample the space of flight for the UAV into N total positions. The UAV i-th position is defined by a vector

p i = [x i , y i , z i ] T ∈ R 3×1 and i ∈ N = {1, . . . , N }.
The mission time for the UAV is sampled to T time slots using a uniform step ∆t. The discrete-time is indexed by t ∈ T = {1, . . . , T }. The takeoff position and time are determined by p γ = [x γ , y γ , z γ ] T and t γ . The UAV reaches the arrival position p δ = [x δ , y δ , z δ ] T with the pre-assigned mission time slots T . The UAV communication link is established using a set of Ground Base Stations (GBS) with fixed locations p g indexed by g ∈ G = {1, . . . , G}. The communication model between the position i and the GBS location g is explained in the next section.

The kinematics and dynamics of the aerial vehicle are not accounted for in this study and they will be considered in our future work. The drone motion is restricted to a moving point in space and time. Therefore, the trajectory modeling is done using a binary variable p ij [t] given in (1) to describe the discrete steps in space and time. The UAV moves between two positions or hovers at the same position (including the start γ and finish δ position) to respect the assigned flight time T of the mission.

p ij [t] = 1 UAV moves from i to j in time slot t, 0 no motion. (1)
The distance between the two positions i and j is given by

d ij = ||p i -p j ||,
where ||.|| is the Euclidean norm operator.

B. Propagation using MKE Diffraction

The geometry description of the MKE problem is shown in "Fig. 2" where each knife-edge can be used to model the elevation point in a mountain (or any other obstacle). We define the height of the g-th GBS, acting as a transmitter, by h g . The height of any i-th position (knife-edge) in the space is defined by h i 1 . We consider K knife edges between g and i. The MKE are characterized by their heights h k , diffracting angles θ k , k ∈ K = {1, . . . K} and the overall distance between g and i given by:

θ ! θ " θ # ℎ $ ℎ ! ℎ " ℎ # ℎ % = ℎ #&! $ ! $ " $ #&! Figure MKE ICC 2023
R = K+1 k=1 r k (2)
The Diffraction Loss (DL) (relative to free space) between g and i overall the distance R is given by Vogler in [START_REF] Vogler | An attenuation function for multiple knife-edge diffraction[END_REF] as:

DL gi (K) = 1 √ π K C K exp(σ K ) ∞ β1 . . . ∞ β K exp(2z)exp - k∈K v 2 k dv 1 . . .dv K (3)
where:

α k = r k r k+2 (r k + r k+1 ) (r k+1 + r k+2 ) 1 2 , k ∈ {1 . . . , K -1}, β k =θ k i (π/λ) r k r k+1 (r k + r k+1 ) 1 2 , k ∈ K, θ k ≈ h k -h k-1 r k + h k -h k+1 r k+1 , k ∈ K, z =      0, K = 1 K k=1 α k (v k -β k )(v k+1 -β k+1 ), K ≥ 2 C K =        1, K = 1 R K k=1 r k r k + r k+1 1 2 , K ≥ 2 σ K = K k=1 β 2 k , (4) (5) (6) (7) (8) (9)
with i = √ -1 is the imaginary number. Expressing exp(2z) [START_REF] Vogler | An attenuation function for multiple knife-edge diffraction[END_REF] is converted from a Kfolded integral into an independent K integral computation. In addition, the author in [START_REF] Vogler | An attenuation function for multiple knife-edge diffraction[END_REF] exploits the recurrsive computation aspect and reaches a closed form using the following identity:

in (3) into a power series as exp(2z) = ∞ m=0 (2z) m m! , the computation of DL gi (K) in
2 √ π ∞ β (v -β) m exp(-v 2 )dv = m!I(m, β), (10)
where m! is the factorial of m and I(m, β) are the repeated integrals of the complementary error function [START_REF] Abramowitz | Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables[END_REF]. A full and detailed proof of the recursive Vogler algorithm for the MKE diffraction is done in [START_REF] Nguyen | On the proof of recursive vogler algorithm for multiple knife-edge diffraction[END_REF]; while, a study case with a closed form expression for K = 4 is provided.

1 previously defined by z i in p i for modeling purposes using the cartesian coordinates and is considered as the terrain elevation in the simulations.

C. Path Loss for Communication Model

In the literature [START_REF] Al-Hourani | Optimal lap altitude for maximum coverage[END_REF], they usually adopt the statistical airto-ground path loss model, which is based on a probability of occurrence in a LoS or NLoS presence between the two communicating nodes. Whereas, the probability is a sigmoidlike function that mainly accounts for the elevation angle between the position of the transmitter and the receiver. As we have explained before, this air-to-ground path loss model is unreralistic to adopt in our case, we formulate the general path loss model that includes the two propagation phenomena, diffraction and LoS by:

PL gi = DL gi (K) 1 b + 4πf c 2 ∥p g -p i ∥ 2 η LoS 1 b (11)
where, f is the system frequency (Hz), c is the speed of light (m/s) and η LoS is the excessive path loss for the LoS (dB) (see [START_REF] Al-Hourani | Optimal lap altitude for maximum coverage[END_REF] for more details). 1(.) is the indicator function, b is a logical variable and b is the negation of b defined by:

b = h (max) > max(h g , h i ) -min(h g , h i ) R . (12)
R is given in (2), h (max) is the maximum value for the heightdistance ratio of the MKE which is formulated to detect the non-LoS and the computation of DL gi (K). h (max) is given by:

h (max) = max k ∈ K \{g, i} h k -min(h g , h i ) k i=1 r i (13)
where \ represents the set minus operator.

III. PROBLEM FORMULATION AND SOLUTION USING

MILP We provide a formulation for the trajectory planning in section III-A based on the previous description of the system model. Then, in section III-B, we define the multiple objectives for the UAV to minimize the travel distance and maximize the communication quality. Finally, the problem is reformulated and solved using the MILP.

A. Problem Formulation

We start by defining the constraints that organize the UAV behavior using

p ij [t]. N j=1 p γj [t γ ] = 1 (14) p ij [t].d ij ≤ V.∆t, ∀i, j ∈ N , ∀t ∈ T (15)
The constraint in (14) defines the UAV departure by imposing the starting location to γ and time to t γ . The constraint in (15) assures that the traveled distance is limited by the drone velocity2 V and the slot duration ∆t.

N i=1 N j=1 p ij [t] ≤ 1, ∀t ∈ T (16)
The constraint in (16) limits the drone motion to one step per time slot. For example, given a time sample t, the UAV is allowed to move from one location i to another j, ∀i, j ∈ N or to stay at the same location i (in this case p ii

[t] = 1, ∀i ∈ N ). N i=1 p il [t] = N j=1 p lj [t + 1], ∀l ∈ N \{δ}, ∀t ∈ {1, . . . , T -1} (17)
The displacement of the UAV with respect to time is guaranteed using the set of flow equations in the constraint (17). For example, if the UAV is at the location l for instant t, it must mandatory move at the time instant t + 1 to any location in N (it can also hover at the same location).

T t=1 N i=1 p iδ [t] = 1 (18)
The arrival at the destination is imposed by the location δ and can be achieved in any time slot from the T set using (18).

N i=1 N j=1 p ij [t]PL (min) j ≤ ξ, ∀t ∈ T (19)
The constraint in (19) impels that the UAV must travel through spatial positions where the path loss satisfies a certain threshold ξ. PL (min) j is the minimum path loss between all the GBSs and the node j and is expressed by:

PL (min) j = min g∈G PL jg (20)

B. Optimization via MILP

The goal is to design the UAV trajectory given the set of parameters and constraints explained in the previous formulation section. The UAV must travel from the departure position to the arrival position given a fixed time. The time mission is defined by the product of the time slots and the duration of each slot T.∆t. The UAV must achieve the following: 1) minimum traveled distance to save power and minimize the time for mission execution; 2) maximum communication quality over the trajectory, by minimizing the threshold ξ for each traveling position p j ∀j ∈ N of the drone. Therefore, we have a multi-objective function to optimize in order to achieve the desired goal. The problem is a Mixed Integer Linear Programming (MILP) and defined by (P): 15), ( 16), ( 17), ( 18), ( 19)

(P) : min pij [t] i,j∈N t∈T ω 1 T t=1 N i=1 N j=1 p ij (t)d ij + ω 2 ξ s.t. (14), (
p ij [t] ∈ B ξ ∈ R + (22) (23) (24)
In ( 22), we use the scalarization method to assign the weights ω 1 and ω 2 for each objective. The weights are applied to control the tradeoff between two metrics; whereas, we can allow enforcing priority either on minimizing the distance or minimizing the path loss threshold.

The solution to the problem (P) is the optimal trajectory given by the vector s * and the scalar ξ * where the elements of s * are defined by the set of values p * ij [t] and given:

S = p * ij [t] | p ij [t] = 1; ∀i, j ∈ N , ∀t ∈ T , ξ * , (25)
where ξ * is the minimum (optimal) path loss value that satisfies the problem settings and outputs the minimum distance trajectory for the drone given by:

D = T t=1 N i=1 N j=1 p * ij (t)d ij (26)
We can use any off-the-shelf MILP solvers to provide the solution to problem (P). One can cite CPLEX or the intlinptog function of Matlab. We should highlight that the MILP is an NP-hard problem to solve, yet such solvers having advanced techniques (different types of cuts, branch and bounds, and heuristics) can achieve solutions to a reasonable scaled problem in a reasonable time. However, we are developing a Dynamic Programming approach to solve this problem in a quasi-optimal way having a polynomial time of execution.

IV. SIMULATION RESULTS

In this section, we present numerical results to test and investigate the proposed approach for UAV trajectory and communication quality optimization in a geographical area located around the French and Spanish border called the Pyrénées mountains and is shown in "Fig. 3". As we can inspect, this terrain presents a complex topography with a lot of mountains of high elevations, the fact that complicates the electromagnetic wave propagation. The selected area is bounded using The first and second corners are specified by the coordinates: (42.46°, 0.85°, 860.8m) and (42.96°, 1.35°, 2246.5m). The latitude and longitude are sampled using an equal step of 0.1°a nd we get in total N = 36 possible navigation positions for the UAV. The departure and arrival locations are fixed to γ = 1 and δ = 34. The time slot of departure is specified by t γ = 1. The mission time is divided into T = 6 slots of equal steps each ∆t = 500 seconds. We have five GBSs (G = 5) distributed randomly in the terrain. We compute the path loss function PL gi ∀g ∈ G, i ∈ N expressed in [START_REF] Nguyen | Deep learning based higher-order approximation for multiple knife edge diffraction[END_REF] using the MKE where K = 3, the operator frequency is f = 2.10 9 Hz, c = 3.10 8 (m/s) and the excessive path loss η LoS = 0.1 (dB). The simulation parameters are summarized in "Tab. I". In "Fig. 4", we plot the elevation profiles to illustrate the terrain between a GBS and a navigation position. The difference of having a position in LoS and NLoS with respect to a GBS is depicted in "Fig. 4a" and "Fig. 4b" respectively. The path loss computation is done for the NLoS situations (i.e. "Fig. 4b") by accounting the diffraction and for the LoS situations (i.e. "Fig. 4a") by accounting the second part in [START_REF] Nguyen | Deep learning based higher-order approximation for multiple knife edge diffraction[END_REF]. The path loss values are shown in "Fig. 5" for N positions and G base stations in different colors. The minimum path loss value PL (min) , at each position p i ∀i ∈ N , for the five GBSs is plotted with blue thick line.

In this scenario, to regulate the tradeoff, the weights in equation ( 22) are selected as follows ω 2 ≫ ω 1 to enforce the a priori on minimizing the threshold ξ of the path loss over the traveled trajectory to guarantee the "best" communication quality in the area. The solution to the problem (P) is given by s * and ξ * = 102.04 dB where: [START_REF] Zhang | Joint trajectory and power optimization for uav relay networks[END_REF] p 16,22 [START_REF] Lee | Trajectory planning for multiple uavs in uav-aided wireless relay network[END_REF] p 22,29 [START_REF] Dat Nguyen | Trajectory control and resource allocation for uav-based networks with wireless backhauls[END_REF] p 29,34 [START_REF] Khawaja | A survey of air-to-ground propagation channel modeling for unmanned aerial vehicles[END_REF] T .

s * = p 1,8 [1] p 8,9 [2] p 9,16
The optimal distance trajectory is computed using (26) and we get D = 74.504 (Km). The optimal trajectory can be observed in the "Fig. 7" and "Fig. 6" for a two and three dimensional visualizations. Additional performance simulations in an extended version of this work will showcase contrasting outcomes with different weights in the objective function, parameter variations, and comparisons to alternative trajectory methods. (min) . The ξ * is the optimal value obtained and plotted in a vertical line

V. CONCLUSION

This paper presents a system model for UAV joint trajectory and communication quality optimization in complicated terrains such mountains and hill range where a complex propogation environement is encoutered. The classical channel modeling in urban and rural zones can not be adopted in such situations where the NLoS aspect is extermly dominant. We propose to use the MKE diffraction phenomenon to retreive a considerable wave energy (that may offer the link continuity) in such topoghraphies to model the channel between the transmitter and the UAV. Then, we formulate the trajectory problem considering the communication quality by using the path loss between the GBSs and the UAV. We define the multiobjective cost to minimize the traveled distance and path loss for each trajectory waypoint and solve the problem using a MILP solver. Numerical investigations are conducted on a selected area of the French border using actual data terrains and randomly distributed GBSs with different elevations. The results reveal that the proposed approach provides the shortest trajectory and the minimum path loss over each waypoint between departure and arrival positions given a mission time. To this end, a "best feasible" communication with the shortest trajectory of a UAV using the diffraction in complicated topographies is achieved.

Fig. 1 :

 1 Fig. 1: The three-dimensional sampled space. The possible navigation positions for the UAV are the yellow circles . The departure and arrival locations are the green circle and the blue square .

FridayFig. 2 :

 2 Fig.2:The MKE diffraction geometry between a GBS and a navigation position for the flying drone where K knife edges is used to account the obstacles.

Fig. 3 :

 3 Fig. 3: Figure representing the 3D terrain visualization for the selected area near the Pyrénées. The positions of interest are represented using the colored circles. The possible navigation positions for UAV are in yellow , the departure in green and the arrival in blue . The GBS positions are represented using the magenta circles two corner locations specified using the latitude, longitude, and elevation expressed in Decimal Degrees (DD) and meters.

Fig. 4 :

 4 Fig. 4: Figure representing the elevetaion in meters between a GBS g and a position p i .

8 Fig. 5 :

 85 Fig. 5: Figure representing the path loss values for each GBS with a fixed color. The blue thick line represents PL(min) . The ξ * is the optimal value obtained and plotted in a vertical line

Fig. 6 :

 6 Fig. 6: Figure representing the UAV optimal trajectory in 3D visualization. The red circles represent the waypoints where the PL (min) j is above the optimally achieved value ξ * . The yellow circles represent the waypoints where the path loss is less or equal to ξ * . The green triangles are the GBSs positions. The optimal found trajectory is in blue dashed line.

TABLE I :

 I Table representing the simulation parameters

This work is supported by the Direction Générale de l'Armement (DGA) and the Agence de l'Innovation de Defense (AID).

assumed constant over time in this study v(t) = V, ∀t ∈ T Authorized licensed use limited to: Universite de Bretagne Occidentale. Downloaded on November 27,2023 at 15:54:38 UTC from IEEE Xplore. Restrictions apply.

Authorized licensed use limited to: Universite de Bretagne Occidentale. Downloaded on November 27,2023 at 15:54:38 UTC from IEEE Xplore. Restrictions apply.

ACKNOWLEDGMENT

The authors would like to thank the Direction Genérale de l'Armement (DGA) and especially the Agence de l'Innovation de Defense (AID) for the financial support of the project "SYDACICO". Fig. 7: Figure representing the UAV optimal trajectory in 2D visualization.


Siegfried Dubois
email: siegfried.dubois@inria.fr

Benjamin Linard

Matthias Zytnicki

Claire Lemaitre

Thomas Faraut

Thomas Faraut Towards

Towards an edit distance between pangenome graphs

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

A variation graph is a data structure that aims to represent variations among a collection of genomes. It is a sequence graph where each genome is embedded as a path in the graph with the successive nodes, along the path, corresponding to successive segments on the associated genome sequence. Shared subpaths correspond to shared genomic regions between the genomes and divergent path to variations: this structure features inversions, insertions, deletions and substitutions. The construction of a variation graph from a collection of chromosome-size genome sequences is a difficult task that is generally adressed using a number of heuristics such as those implemented in the state-of-the-art pangenome graph builders minigraph-cactus [START_REF] Hickey | Pangenome Graph Construction from Genome Alignment with Minigraph-Cactus[END_REF] and pggb [START_REF] Garrison | Unbiased pangenome graphs[END_REF]. The question that arises is to what extent the construction method influences the resulting graph and therefore to what extent the resulting graph reflects genuine genomic variations.

We propose to address this question by constructing an edition script between two variation graphs built from the same set of genomes which provides a measure of similarity, and more importantly that enables to identify discordant regions between the two graphs. We proceed by comparing, for each genome, the two corresponding paths in the two graphs which correspond to two possibly different segmentations of the same genomic sequence. As such, for each interval defined by the nodes of the path of the genome in the first graph, we define a set of relations with the nodes of the second graph, such as equalities, prefix and suffix overlaps. . . which allows for a calculation of how many elementary operations, such as fusions and divisions of nodes, are required to go from one graph to another.

We tested our method on variation graphs constructed using both simulated dataset as well as a real dataset made of 15 yeast telomere-to-telomere phased genome assemblies [START_REF]Telomere-to-telomere assemblies of 142 strains characterize the genome structural landscape in Saccharomyces cerevisiae[END_REF], with minigraph-cactus as the graph construction tool. This tool builds iteratively the variation graph, starting from a genome taken as a reference and incorporating each genome in the order provided by the user. In this work, we compared by pairs the graphs constructed from the same set of genomes but using different incorporation orders. After the application of our algorithm, we get a measure of the similarity between each pair of variation graphs in the form of a 1 Towards an edit distance between pangenome graphs distance, that enables both to quantify the impact of the order of genomes in the graph construction, and to pinpoint the specific areas of the graph and genomes that are impacted by the changes in segmentation. Ongoing work includes being able to compare graphs issued from different variation graphs construction tools.

Availability: This algorithm is implemented as a Python tool: https://github. com/Tharos-ux/pancat


Sylvain Verron
email: sylvain.verron@univ-angers.fr

Mohamed Salim Bidou

Laetitia Perez

Laurent Autrique

Heat sources failure instant estimation: comparison of Kalman smoothing and supervised learning

Keywords: Fault Detection, Kalman filter, multiple regression, partial differential equations

Fault detection has become a critical aspect in industrial systems due to the increased complexity and safety concerns. This paper focuses on the potential failure of a fixed heat source located on a thin aluminum plate, with the added difficulty of another non-failing heat source being present on the same plate. Only three fixed sensors are integrated to the plate, which is considered a 2D problem. The objective of this study is to compare two approaches for estimating the failure instant of the heat source. The first approach uses a Kalman filter, followed by a smoothing phase and an exploitation phase to better estimate the failure instant. The second approach is a supervised learning method using multiple regression, where the relationship between the failure instant and the observed sensor data is established through a training dataset generated using the model developed for the Kalman filter. The proposed application considers a 1m x 1m aluminum plate with 3mm thickness, 3 sensors and 2 heat sources, with an observation time of 3600 seconds. The effect of measurement noise on the identification of defects is analyzed for different signal-to-noise ratios through Monte-Carlo simulations.

INTRODUCTION

Fault detection has become a crucial area of research over the past two decades due to the increasing complexity of industrial systems and the growing concern for their safety. The detection of faults in complex physical systems is typically achieved by knowledge models based on partial differential equations (PDEs) [START_REF] Isermann | Fault-Diagnosis Systems From Fault Detection to Fault Tolerance[END_REF]. In the field of thermic, for instance, heat exchange is described by Fourier's law, which results in a system of PDEs. Conventional thermal studies usually consider fixed or mobile heat sources in a finite dimensional space [START_REF] Massard | Estimation of position dependent transient heat source with the kalman filter[END_REF].

In this paper, we focus on the potential failure of a fixed heat source located on a thin aluminium plate, which can be considered a 2D problem. A challenging aspect of this study is the presence of another heat source, considered to be non-failing, on the plate. Additionally, we make the assumption that only 3 fixed sensors (with defined and fixed positions) are integrated into the plate [START_REF] Bidou | Identification of failure times for a system governed by a non-linear parabolic partial differential equation[END_REF].

The objective of this paper is to compare two methods for estimating the instant of failure of the heat source. The first approach we develop is based on a Kalman filter, followed by a smoothing phase and an exploitation phase of the latter to better estimate the failure instant a posteriori [START_REF] Bidou | Kalman smoother for detection of heat sources defects[END_REF]. To model the problem as a Kalman filter (linear dynamical system), a modelling step is necessary. For this, we will use the finite difference method [START_REF] Grossmann | Numerical Treatment of Partial Differential Equations[END_REF].

The second proposed method is a supervised learning method, a multiple regression, exploiting the heat evolution model developed for the Kalman filter. For this, a training dataset is generated using the defined model, in which we simulate different possible failure times. The regression will then establish the link between the failure instants and the observed sensor data [START_REF] Duda | Pattern Classification[END_REF].

The proposed application is an aluminium plate 1 meter by 1 meter, 3mm thick, with 3 sensors and 2 supposedly known heat sources. The observation time is 3600 seconds, after which the proposed methods must announce the estimated instant of failure of the source of interest. An interesting point is that the frequency of sensors reading is low: every 9s. Particular attention is paid to the effect of measurement noise on defect identification to highlight the relevance of the two approaches. Several signal-to-noise ratios are considered through an analysis based on Monte-Carlo simulations.

Figure 1 show the position of the 2 sources and the positions of the three sensors. On figure 2, one can view the heat flux of each source, for normal operating conditions (no failure).

METHODS

This methodology section will be subdivided into several subsections. We will first approach the method of modelling the phenomenon of heat diffusion by the finite difference approach. Indeed, this modelling in the form of a linear system will be exploited by the two types of methods proposed to estimate the instant of failure of the heat source. The first proposed method will exploit the power of the Kalman filter and smoother, followed by an optimization phase. The third subsection will present a classic machine learning approach, namely multiple regression.

Finite difference modelling

The finite difference method is a numerical approach to solving differential equations. The principle is to cut the plate into a finite number of small segments, or elements, and to use mathematical approximations to represent the conditions at each edge of these elements.

In our application, temperature evolution is described [START_REF] Massard | Estimation of position dependent transient heat source with the kalman filter[END_REF] by:

𝜌𝐶 𝜕𝑇 𝜕𝑡 -𝜆 𝜕 2 𝑇 𝜕𝑥 2 -𝜆 𝜕 2 𝑇 𝜕𝑦 2 = 𝐺 𝑒 - 2ℎ(𝑇-𝑇 0 ) 𝑒 ( 1
)
Where 𝑇 is temperature (𝑇 0 is the initial one), 𝑡 is time, 𝜌𝐶 is the heat density, 𝜆 is the thermal conductivity (considered as constant in this study), 𝑒 is the thickness of the plate, ℎ is the convective transfer coefficient, and finally, 𝐺 is the heating flux.

To model a metal plate with the finite difference method, we discretize the plate to adapt it to a numerical model. For that, we define temperature in each discretised point {x=i, y=j}, at instant 𝑘 by 𝑇 = 𝑇 𝑖,𝑗 𝑘 . So, we can apply the finite difference method in order to approximate the first and second derivatives:

𝜕𝑇 𝑖,𝑗 𝑘 𝜕𝑡 ≈ 𝑇 𝑖,𝑗 𝑘+1 -𝑇 𝑖,𝑗 𝑘 ∆𝑡 ( 2
)
𝜕 2 𝑇 𝜕𝑥 2 ≈ 𝑇 𝑖-1,𝑗 𝑘 -2𝑇 𝑖,𝑗 𝑘 +𝑇 𝑖+1,𝑗 𝑘 ∆𝑥 2 (3)
𝜕 2 𝑇 𝜕𝑦 2 ≈ 𝑇 𝑖,𝑗-1 𝑘 -2𝑇 𝑖,𝑗 𝑘 +𝑇 𝑖,𝑗+1 𝑘 ∆𝑦 2 (4)
Where ∆𝑡 is the time step, and Δx and ∆𝑦 are the spatial steps on respectively the 𝑥 dimension and the 𝑦 dimension. Same discretization is done for flux heat 𝐺 = 𝐺 𝑖,𝑗 𝑘 .

Using these formulas, we can construct a system of linear equations representing the temperature conditions at each edge of each element. This system can be solved to determine the temperature at each location and time, giving us a numerical approximation of the solution to the original differential equation.

𝑇 𝑖,𝑗 𝑘+1 = (1 -

Note that for a point in the domain, its temperature at time k+1 will depend on:

•Its own temperature at time k •The temperature at time k of its neighbours (right/left/top/bottom) •The heat flux at time k at this point •The constant linked to h For computational purposes, we rewrite the problem in the form of a state evolution model and sequentially rearrange all nodes (i, j) with indices m = 1,...,M. where M =I × J. Thereby, our application could be modelled as a state representation of a discrete time invariant linear system:

{ 𝑻 𝑘+1 = 𝑨. 𝑻 𝑘 + 𝑩. 𝑮 𝑘 + 𝑯 𝑻 𝒐𝒃𝒔 𝑘 = 𝑪. 𝑻 𝑘 (6)
Where 𝑻 𝑘 is a matrix containing temperature of all discretised points of the plate at the instant 𝑘, 𝑮 𝑘 is a matrix containing heat flux values (2 sources 𝑔1 and 𝑔2) at the instant 𝑘, 𝑨 is a matrix allowing to take into account the temperature (with specific coefficient) of neighbours points to compute temperature at next instant step, 𝑩 and 𝑪 matrices are coding respectively, the positon of the sources on the plate and the position of the sensors on the plate. 𝑯 is a constant vector of same value (

∆𝑡.2ℎ.𝜃 0 𝜌𝐶.𝑒 ).

𝑻 𝒐𝒃𝒔

𝑘 is a matrix containing the value of the three sensors at instant k.

This modeling, also classically called "direct problem", unlike the inverse problem, will make it possible to simulate the system, to observe its behaviour, for different configurations (in particular different cases of failures). Some modeling parameters can cause the results to differ somewhat, in particular the step of discretization of the physical plate ∆𝑥 and ∆𝑦, or the step of calculation time ∆𝑡.

For example, if it is assumed that a failure of source 1 occurred at 𝑡 = 1500𝑠, the evolution of the temperatures at the three sensors are shown in figure 3 (observations from sensors are subject to a Gaussian noise of standard deviation of 0.5).

First approach: Kalman Smoothing

The Kalman filter is a mathematical algorithm used to estimate the state of a dynamic system from noisy measurements [START_REF] Kalman | A new approach to linear filtering and prediction problems[END_REF]. It is a recursive algorithm that uses a prediction step to estimate the state at the next time step based on the current state and a control input, followed by a correction step that updates the state estimate based on the measurement.

As we have modelled our application as a dynamical system (equation ( 6)), we can use the Kalman filter. But we can see that in this case, we need to know 𝑮 𝑘 for each instant. However, real values of 𝑮 𝑘 are not known, this is particularly what we would like to estimate: 𝑔1 and 𝑔2. So, in this context, we reformulate the dynamical system in order to integrate the 𝑮 𝑘 matrix in the state vector [START_REF] Berg | Force Estimation via Kalman Filtering for Wind Turbine Blade Control[END_REF]. For that, we reformulate our equation ( 6), as presented in equation ( 7) below.

{ [ 𝑻 𝑘+1 𝑮 𝑘+1 ] = 𝑨 ′ . [ 𝑻 𝑘 𝑮 𝑘 ] + 𝑯 + 𝒘 𝒌 𝑻 𝒐𝒃𝒔 𝑘 = 𝑪 ′ . [ 𝑻 𝑘 𝑮 𝑘 ] + 𝒗 𝒌 (7)
Where: 𝑨 ′ = [ 𝑨 𝑩 𝟎 𝟏 ] and 𝑪 ′ = [ 𝑪 𝟎 ], 𝒘 𝒌 and 𝒗 𝒌 are respectively the process noise and the observation noise, assumed to be Gaussian from mean zero and covariance matrices 𝑸 and 𝑹 . We name 𝝁 ̂𝑘 and 𝚺 ̂𝑘 the estimate of, respectively, the mean and covariance matrix of the state vector where 𝑰 is the identity matrix and 𝑻 denotes the transpose.

Under the assumption that the entire time horizon observations are available, it is possible to refine estimation of 𝝁 ̂𝑘 and 𝚺 ̂𝑘 with the application of the Kalman smoother (also named RTS smoother) [START_REF] Murphy | Machine learning: a probabilistic perspective[END_REF].

As opposed to just the current measurement used in the Kalman filter, the Kalman smoother is an algorithm that provides a more accurate estimate by using the entire sequence of measurements. The Kalman smoother can be seen as a backward pass of the Kalman filter, using the same prediction and correction steps, but using the corrected estimates from the future time steps to improve the estimates at the current time step. The Kalman smoother algorithm can be formulated as follows:

From the Kalman filter algorithm, start from the last estimates: 𝝁 ̂3600 and 𝚺 ̂3600 , and for each k from 3599 to 1: 𝑷 𝑘 = 𝚺 ̂𝑘|𝑘 𝑨′ 𝑻 𝚺 ̂𝒌+𝟏|𝒌 -𝟏 𝝁 ̂𝑘|1:3600 = 𝝁 ̂𝑘|𝑘 + 𝑷 𝑘 (𝝁 ̂𝑘+1|1:3600 -𝝁 ̂𝑘+1|𝑘 ) 𝚺 ̂𝑘|1:3600 = 𝚺 ̂𝑘|𝑘 + 𝑷 𝑘 (𝚺 ̂𝑘+1|1:3600 -𝚺 ̂𝑘+1|𝑘0 )𝑪′ 𝑻

We will name 𝑔1 ̂ the estimated signal composed of all k 𝝁 ̂𝑘|1:3600 . We have to identified the failure instant based on this signal, and knowing also the normal operating conditions, said theoretical 𝑔1. So, an optimization phase of the estimation of the failure instant 𝑡 𝑓𝑎𝑖𝑙 , based on the minimization of a root mean square criteria between the 𝑔1 ̂ estimate signal and possible faulty signals (one can see [START_REF] Bidou | Kalman smoother for detection of heat sources defects[END_REF] for more details).

For illustration of this methodology, we simulate an example of a failure of source 1 at 𝑡 = 1500𝑠. Available data is composed of the no fault g1 signal (theoretical g1), and of the data from the 3 sensors during the 3600 seconds, sampled every 9 seconds, giving 400 observed instants (with a noise sensor of 𝜎 = 0.5).

Firstly, on figure 4, we can plot the data from the 3 sensors. Secondly, from this data, we can apply he Kalman filter algorithm, followed by the Kalman smoother algorithm. Each of these algorithms, give an estimate of g1, but evidently, estimation from the smoother are the better one because this algorithm takes into account all possible measurements. The two estimations of g1 are represented on figure 5. Finally, figure 6 presents the global results after the search phase of the estimation of the failure instant 𝑡 𝑓𝑎𝑖𝑙 . On this figure, we can observe that the failure instant estimate is 𝑡 𝑓𝑎𝑖𝑙 = 1491𝑠, which is very satisfying compared to the real failure instant of 1500s.

Second approach: Multiple regression

Multiple regression is a machine learning algorithm used to predict one dependent variable (i.e. output or target variable) from multiple independent variables (i.e. inputs or variables explanatory) [START_REF] Duda | Pattern Classification[END_REF].

The main objective of multiple regression is to find the best line that represents the relationships between the independent variables and the dependent variable. This line is called the regression function. The multiple regression model can be represented mathematically as follows: 𝑦 = 𝛽 0 + 𝛽 1 𝑥 1 + 𝛽 2 𝑥 2 + ⋯ + +𝛽 𝑛 𝑥 𝑛 + 𝜀 Where 𝑦 is the dependent variable (output), 𝑥 1 , 𝑥 2 , … , 𝑥 𝑛 are the independent variables (inputs), 𝛽 0 , 𝛽 1 , 𝛽 2 , … , 𝛽 𝑛 are the regression coefficients, 𝜀 is the random error that takes into account unexplained influences on the dependent variable.

The objective of a regression learning will be to find the coefficients 𝛽 0 , 𝛽 1 , 𝛽 2 , … , 𝛽 𝑛 which minimize the error between the predicted value and the actual value of the dependent variable. Optimization algorithms such as gradient descent or least squares can be used to find the optimal coefficients.

We will now explain how we use multiple regression to solve the problem of estimating the time of failure of a source. Indeed, in our problem, the instant of failure will be the variable to be predicted (𝑦 = 𝑡 𝑓𝑎𝑖𝑙 ). The descriptive variables will be the values of the 3 sensors registered over the period studied (1 hour).

In order to create a useful regression model, it is not possible to use a history since that would never cover the different possible failure times. Thus, we will use the modeling of the phenomenon (equation ( 6)) to generate/simulate different failure cases, and this for different sensor noise levels. The generation of this simulated history proceeds according to the following indications.

A possible instant of failure 𝑡 𝑓𝑎𝑖𝑙 is randomly drawn over the period studied (3600s). The system is then simulated including the failure of source 1 at time 𝑡 𝑓𝑎𝑖𝑙 . The values of the sensors C1, C2 and C3 are then recorded over the entire period. So, we obtain a number of 𝑡𝑜𝑡𝑎𝑙 𝑡𝑖𝑚𝑒 × 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑠𝑒𝑛𝑠𝑜𝑟𝑠 𝑠𝑎𝑚𝑝𝑙𝑖𝑛𝑔 𝑡𝑖𝑚𝑒 ie 3600×3/9=10800/9=1200 descriptors. Repeat this procedure for a desired number of observations, at least greater than number of descriptors.

As with all supervised learning techniques, an important step in the application of this regression will be the selection of components (descriptors), thus making it possible to make the model more robust and provide better performance. Indeed, it is certain that among the 1200 descriptors used to estimate the instant of failure, some are much less informative than others, but still bring noise. Many component selection methods exist in the literature, generally classified into two types: wrapper and filter. Since the subject of this article is not the evaluation of this type of technique, we have chosen a classic evaluation of the importance of descriptors: univariate feature ranking for regression using Ftests. We then selected only the best descriptors.

RESULTS

In order to compare the two presented approaches (Kalman smoother and Linear regression), we propose different configurations. For each configuration, all simulations were performed on Matlab software.

The modeling parameters making it possible to solve the direct problem (finite differences) were chosen as follows: time step ∆𝑡 = 1 𝑠, and ∆𝑥 = ∆𝑦 = 0.1 𝑚.

The first step is to use finite difference modeling to generate the history. The number of individuals in this history was chosen to be 5000. Once the history was created, we applied the Univariate feature ranking for regression using F-tests algorithm, allowing us to see the importance of each descriptor with respect to the instant of failure variable. The result of this evaluation can be seen in Figure 7. We thus clearly see that certain descriptors are not at all informative. We therefore made the choice to select only those that provided a lot of information.

Figure 7. univariate feature ranking using F-tests For 30 simulations, we have run, on the same data, the two presented methods. We give, in table 1, the results for 3 different level of sensor noise: 𝜎 = 0.1, 𝜎 = 0.5 and 𝜎 = 1. So, in order to see the impact of such a parameter, for each configuration, we give results in term of mean and standard deviation (in brackets) on 30 simulations. As we can see in table 1, the Kalman smoother method is much more efficient than linear regression. Indeed, even if for most cases the averages of the simulations are comparable, we clearly see that the standard deviation for the linear regression method is significantly higher than for the Kalman smoother.

Another fact, absolutely prohibitive for the use of linear regression on this type of problem, is the fact that this technique cannot correctly diagnose a fault on a heat source other than source one. Indeed, if we wanted to take this possible technique to diagnose the failure of source 1 and source 2, it would amount to creating a virtual history with not 3600 possible failure instants (those of source one), but the combination of 3600 × 3600 possible failure times, then leading to a combinatorial explosion (almost 13 million cases). Moreover, the Kalman smoother technique will be able to diagnose failures but also restarts of sources 1 and 2.

CONCLUSIONS

In this article, we proposed to compare 2 approaches to solve the problem of identifying an instant of failure of a heat source on a fixed plate equipped with 3 sensors. These 2 approaches, the smoother of Kalman as well as the linear regression, required the creation of a model based on the finite differences. In the case of linear regression, this model is used to generate a simulated example database, this base then being used to correctly estimate the coefficients of a regression model. In the case of the Kalman smoother, the model is seen as a dynamic linear system, thus allowing an estimation of the flux of each of the heat sources. In order to compare the 2 approaches, 30 simulations of the system with a failure at time 1500 seconds were studied. Although on average the 2 techniques are very close to a diagnosis at 1500 seconds, the Kalman smoother is much more efficient because the standard deviation over the 30 simulations is much lower than for linear regression.

Figure 1 .Figure 2 .

 12 Figure 1. Sources and Sensors Positions

Figure 3 .

 3 Figure 3. Temperatures without failure and without noise (continuous) and with failure and noise (points)

  [ 𝑻 𝑘𝑮 𝑘 ]. With the transformed linear system of equation[START_REF] Kalman | A new approach to linear filtering and prediction problems[END_REF], it becomes possible to apply the Kalman filter and estimate 𝝁 ̂𝑘, for each instant k, and so the temperature, but moreover the flux of the sources. The Kalman filter steps are described below:Initialize the estimates: 𝝁 ̂0 = [ 𝑻 0 𝑮 0 ] and 𝚺 ̂0 = [𝟎] For each k from 1 to 3600:𝝁 ̂𝑘|𝑘-1 = 𝑨′𝝁 ̂𝑘-1|𝑘-1 + 𝑯 𝚺 ̂𝑘|𝑘-1 = 𝑨′𝚺 ̂𝑘-1|𝑘-1 𝑨′ 𝑻 + 𝑸𝑲 𝑘 = 𝚺 ̂𝑘|𝑘-1 𝑪′ 𝑻 (𝑪 ′ 𝚺 ̂𝑘|𝑘-1 𝑪′ 𝑻 + 𝑹) -𝟏 𝝁 ̂𝑘|𝑘 = 𝝁 ̂𝑘|𝑘-1 + 𝑲 𝑘 (𝑻 𝒐𝒃𝒔 𝑘 -𝑪′𝝁 ̂𝑘|𝑘-1 ) 𝚺 ̂𝑘|𝑘 = (𝑰 -𝑲 𝑘 𝑪′)𝚺 ̂𝑘|𝑘-1

Figure 4 .Figure 6 .

 46 Figure 4. Available data

Table 1 .

 1 Monte-Carlo simulations results

		Kalman	Linear
		Smoother	Regression
		𝑡 𝑓𝑎𝑖𝑙	𝑡 𝑓𝑎𝑖𝑙
	𝜎 = 0.1 1495,1(1,69)	1506,2 (6,53)
	𝜎 = 0.5 1494,9(11,09) 1508,0 (40,3)
	𝜎 = 1	1500,3 (14,61) 1514,9 (66,65)


A Nazih

Saida Krimi

Stanislav Pechev

Matias Velázquez

Michel Couzi

Abdelaziz El

Crystalline and vitreous Na 3.89 Ca 0.67 Al 0.23 Ti 0.77 (PO 4 ) 3 : Synthesis, crystal structure, vibrational and UV-Visible spectra

Keywords: 77(PO4)3 : Synthesis, crystal structure, vibrational and UV-Visible spectra NaCaAlTiPO-phosphate, Nasicon, Nasiglass, Structure, Raman, Infrared, UV-Visible

Crystalline and vitreous

Na3.89Ca0.67Al0.23Ti0.


Jean-Pierre Quenot
email: jean-pierre.quenot@chu-dijon.fr

Idris Amrouche

Jean-Yves Lefrant

Kada Klouche

Samir Jaber

Damien Du Cheyron

Jacques Duranteau

Julien Maizel

Eric Rondeau

Etienne Javouhey

Damien Du Cheyron

Théophile Gaillot

René Robert

Jean Dellamonica

Bertrand Souweine

Julien Bohé U Saber

Davide Barbar

Caroline Sejourné

Christophe Vinsonneau

Renal Replacement Therapy for Acute Kidney Injury in French Intensive Care Units: A Nationwide Survey of Practices

Keywords: Renal replacement therapy, Acute kidney injury, Intensive -care unit, Survey of practice

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

Background

The frequency of acute kidney injury (AKI) can be as high as 50% in the intensive care unit (ICU) and is an independent risk factor for mortality [START_REF] Clec'h | Multiple-center evaluation of mortality associated with acute kidney injury in critically ill patients: a competing risks analysis[END_REF][START_REF] Poukkanen | Variation in the use of renal replacement therapy in patients with septic shock: a substudy of the prospective multicenter observational FINNAKI study[END_REF][START_REF] Hoste | Epidemiology of acute kidney injury in critically ill patients: the multinational AKI-EPI study[END_REF][START_REF] Mehta | International Society of Nephrology's 0by25 initiative for acute kidney injury (zero preventable deaths by 2025): a human rights case for nephrology[END_REF][START_REF] Ronco | Acute kidney injury[END_REF]. Mortality is reported to be between 40% and 60% in ICU patients with AKI [START_REF] De Mendonca | Acute renal failure in the ICU: risk factors and outcome evaluated by the SOFA score[END_REF][START_REF] Uchino | Acute renal failure in critically ill patients: a multinational, multicenter study[END_REF] despite recent improvements in our understanding of the pathophysiological mechanisms [START_REF] Gomez | A unified theory of sepsis-induced acute kidney injury: inflammation, microcirculatory dysfunction, bioenergetics, and the tubular cell adaptation to injury[END_REF] and the implementation of renal protective measures [START_REF] Mehran | Contrast-associated acute kidney injury[END_REF]. If uncorrected, and/or in the presence of metabolic disorders refractory to medical therapy, AKI may necessitate renal replacement therapy (RRT), in about 20% of ICU situations [START_REF] Clec'h | Multiple-center evaluation of mortality associated with acute kidney injury in critically ill patients: a competing risks analysis[END_REF][START_REF] Poukkanen | Variation in the use of renal replacement therapy in patients with septic shock: a substudy of the prospective multicenter observational FINNAKI study[END_REF][START_REF] Hoste | Epidemiology of acute kidney injury in critically ill patients: the multinational AKI-EPI study[END_REF][START_REF] Nisula | Incidence, risk factors and 90-day mortality of patients with acute kidney injury in Finnish intensive care units: the FINNAKI study[END_REF]. However, practices are extremely heterogeneous [START_REF] Legrand | Management of renal replacement therapy in ICU patients: an international survey[END_REF][START_REF] Jamal | A national survey of renal replacement therapy prescribing practice for acute kidney injury in Malaysian intensive care units[END_REF][START_REF] Fealy | Continuous renal replacement therapy: current practice in Australian and New Zealand intensive care units[END_REF][START_REF] Clark | Renal replacement therapy practices for patients with acute kidney injury in China[END_REF][START_REF] Heung | CRRTnet: a prospective, multi-national, observational study of continuous renal replacement therapy practices[END_REF][START_REF] Digvijay | International survey on the management of acute kidney injury and continuous renal replacement therapies: year 2018[END_REF][START_REF] Murugan | Net ultrafiltration prescription and practice among critically Ill patients receiving renal replacement therapy: a multinational survey of critical care practitioners[END_REF], likely due to the fact that most international guidelines date from 10 or more years ago, and do not focus on RRT in detail [START_REF] Brochard | An official ATS/ERS/ESICM/SCCM/SRLF statement: prevention and management of acute renal failure in the ICU patient: an international consensus conference in intensive care medicine[END_REF][START_REF]Kidney Disease: Improving Global Outcomes (KDIGO) Acute Kidney Injury Work Group. KDIGO clinical practice guideline for acute kidney injury[END_REF]. In addition, it may be difficult to integrate more recent literature on this topic into routine clinical practice.

In France, national recommendations for RRT in the ICU were published in 2015 [START_REF] Vinsonneau | Renal replacement therapy in adult and pediatric intensive care: recommendations by an expert panel from the French Intensive Care Society (SRLF) with the French Society of Anesthesia Intensive Care (SFAR) French Group for Pediatric Intensive Care Emergencies (GFRUP) the French Dialysis Society (SFD)[END_REF] but it remains unclear how they are applied in daily practice. While there is little debate about the emergency indication for RRT, there is much greater controversy regarding other points [START_REF] Ahmed | Renal replacement therapy in the critical care setting[END_REF], such as the timing of RRT initiation, the technique to use, the dose of dialysis, anticoagulation of the dialysis circuits, and the type of catheter. In order to obtain insights into actual current practices in terms of RRT for AKI in the ICU in France, we performed a national survey of practices among a nationwide network of experts.

Methods

The study was performed from November 15, 2019, to January 24, 2020. Using the SurveyMonkey platform (www.surveymonkey.com), we sent an electronic questionnaire to all the chiefs of ICU in France caring for patients with AKI and who were equipped with facilities to provide RRT (continuous or intermittent). The questionnaire was developed on the basis of the different recommendations stipulated in the national guidelines [START_REF] Vinsonneau | Renal replacement therapy in adult and pediatric intensive care: recommendations by an expert panel from the French Intensive Care Society (SRLF) with the French Society of Anesthesia Intensive Care (SFAR) French Group for Pediatric Intensive Care Emergencies (GFRUP) the French Dialysis Society (SFD)[END_REF]. It was piloted on a group of ICU physicians (the scientific committee of the study, comprising the authors of the present publication) to verify readability and feasibility. The Scientific Committee for the study comprising experts in the field of intensive care verified the exhaustiveness of the list of centers to be contacted throughout the country, using mailing lists of physicians and departments affiliated to national professional societies. The scientific committee members also sent reminders to colleagues who did not respond after the first contact.

Questionnaire Structure

The questionnaire comprised 2 sections. The first section of the questionnaire was completed by the Department Chief and comprised 42 questions about the organizational aspects of the ICU, standard procedures, and training. Once the Department Chief had completed the first section and provided consent for the second stage, the second section of the questionnaire was completed by the ICU physicians in the participating departments (designated by the Department Chief). This section investigated individual practices in terms of prescription and implementation of RRT in the ICU. The second section was only made available to the designated physicians in the ICU after the Department Chief had completed Section 1. A total of 4 reminders were sent during the study period to ensure a maximum response rate.

In response to multiple-choice questions, we categorized responses with a frequency of response >75% as representing "the majority of cases," and between 50 and 75%, the predominant modality. For questions concerning indications, characteristics, and the choice of RRT technique, responses were categorized into "Strongly or moderately agree," "Strongly or moderately disagree," and "Neutral."

Data on the volume of activity (admissions and number of RRT sessions) date from 2018 since the activity of 2019 was not available at the time this study was initiated. Given the design of the study as a survey of professional practices, informed consent was not required in accordance with the French law. Quantitative data are reported as medians and interquartile range or numbers and percentage (%).

Results

Questionnaire Section 1: Participating Institutions

We identified 356 ICUs, and among these, 88 (24.7%) Department Chiefs completed Section 1 of the questionnaire, corresponding to 88 ICUs. From these 88 ICUs, 285 physicians were contacted to complete Section 2, of whom a total of 232 responded (82%). The characteristics of the participating ICUs (N = 88) and physicians (N = 232) are shown in Table 1.

Questionnaire Section 1: RRT Practices at ICU Level

Among the 88 ICUs participating in the study, 48% (42/88) of Department chiefs declared that RRT (either continuous or intermittent) had been used in fewer than 100 patients, and 9% (8/88) declared the use of RRT in more than 200 patients during the year 2018. The availability of continuous and intermittent RRT was 79% (69/88) and 87% (76/88), respectively, among participating institutions. Regarding Sustained Low-Efficiency Dialysis (SLED), it was used in only 14% (12/88) of responding ICUs. Of note, a written protocol existed for management of AKI in only 37% (33/88) of ICUs. The organization of RRT initiation (continuous or intermittent), the type of material used (membrane, lock, and catheter insertion), and the management of dialysate production for intermittent RRT are detailed in Table 2.

For intermittent RRT, the ICU nurses were reported to monitor the sessions in 83% (73/88) of centers. An operational roster for a nurse to be on duty at night and during the weekends for the implementation of RRT was available in 20% (18/88) of participating ICUs. According to the Department Chiefs who responded to this survey, training in RRT was made available to physicians in <20% of cases, whereas 80% (70/88) of units organized training for nurses in RRT via expert practitioners, simulation, and/or a specific university diploma.

In terms of individual practices, regarding the preferred vascular approach for RRT, the right internal jugular vein was most popular (82%), followed by the femoral vein (16%) and in very few cases the left internal jugular vein (2%). No respondent cited use of the subclavian approach. The most commonly used diameter was >12 Fr in 70% of cases, with length >24 cm via the femoral approach in 92% of cases. The use of antimicrobial-impregnated catheters was not cited. According to 62% of respondent physicians, insertion of the RRT catheter is mainly performed by the resident and largely under echographic guidance (96%). In pediatrics, the size of the dialysis catheters was predominantly 6.5 Fr for children weighing 3-6 kg (76%) and 7-10 kg (50%), and 8 Fr for children weighing 11-20 kg (72%) or 20-30 kg (50%), and 11.5 Fr for children weighing >30 kg (51%).

Individual Practices Reported in Terms of RRT Technique and Prescription

The main reasons justifying the choice of RRT and the criteria for initiating RRT (emergency or nonemergency) are presented in Figures 123. Intermittent RRT was preferred as the firstline option (56%) in a patient with single organ failure (i.e., kidney) at the acute phase, followed by continuous RRT in 33% and SLED in only 4%. In patients with septic shock, continuous RRT was predominantly used, with continuous veno-venous hemofiltration in 46%, continuous veno-venous hemodialysis in 33%, continuous veno-venous hemodiafiltration in 17%, and HVCVVH (4%).

In patients with multi-organ failure, the techniques of choice were mainly continuous venovenous hemofiltration (25%), intermittent RRT (19%), continuous venovenous hemodialysis (17%), and continuous veno-venous hemodiafiltration (13%). In hemodynamically stable patients, intermittent RRT was predominantly preferred (47%) over continuous RRT (26%) and SLED (2.7%).

In pediatrics, 51% of responding physicians reported that they used peritoneal dialysis in case of the need for RRT. In case of heparin-induced thrombocytopenia, danaparoid sodium was predominantly used (77%). The most frequent criterion for weaning from RRT was diuresis, followed by a drop in urea, and urinary markers (urea and creatinine) (Fig. 4). Of note, assessment of renal function recovery is usually performed at the end of the ICU stay (35%), or after discharge from the ICU during a consultation with a nephrologist (74%).

Individual Practices in Terms of Prescription according to the Technique Used

Intermittent RRT

Intermittent RRT for AKI is prescribed by 72% of physicians according to the patient's needs, 3 times a week by 20% and daily by 8%. Blood flow and dialysate for intermittent RRT are prescribed at, respectively, 200-300 mL/ min and between 400 and 600 mL/min. The majority of physicians (94%) prescribe an intermittent RRT duration of between 3 and 6 h, and 62% of physicians using a membrane surface area between 1.3 m2 and 2 m2. In patients at high hemorrhagic risk, 32% performed filter rinsing. In patients at low risk of hemorrhage, low molecular weight heparin (73%) and unfractionated heparin (25%) are preferred over citrate (2%). Intermittent RRT performed on an arteriovenous fistula is possible in the ICU (71%) and requires the involvement of a nurse from the nephrology unit, to puncture and attach the machine (62%). Of note, when an arteriovenous fistula is present, intermittent RRT sessions are prescribed by the ICU physicians in 86% of cases.

Continuous RRT

Prescribed blood flow was between 100 and 250 mL/ min (83%) and dialysate flow was predominantly prescribed according to the patient's weight (80%). The effluent flow rate (substitution fluid + dialysate + net ultrafiltration) is set between 1,000 and 4,000 mL/h (93%) and pre-or post-dilution was reportedly performed by 60% of respondents. The dialysis dose was 25-35 mL/kg/h for 65% of respondents. The RRT circuit was generally anticoagulated using citrate, both in patients with high hemorrhagic risk (79%) and in those with low hemorrhagic risk (67%).

Discussion

The DIAM study is the first survey of practices to be performed in France since the publication of the national guidelines for RRT in adults and children in the ICU [START_REF] Vinsonneau | Renal replacement therapy in adult and pediatric intensive care: recommendations by an expert panel from the French Intensive Care Society (SRLF) with the French Society of Anesthesia Intensive Care (SFAR) French Group for Pediatric Intensive Care Emergencies (GFRUP) the French Dialysis Society (SFD)[END_REF]. Our study provides insights into current practices, which may have evolved in recent years in response to new publications in the literature.

In particular, a point where the state of knowledge has evolved is the timing of RRT initiation in the ICU. In emergency situations (e.g., hyperkalemia, metabolic acidosis, pulmonary edema refractory to medical therapy, or lysis syndrome), the findings reported in our survey regarding prescription of RRT are coherent with guidelines [START_REF] Vinsonneau | Renal replacement therapy in adult and pediatric intensive care: recommendations by an expert panel from the French Intensive Care Society (SRLF) with the French Society of Anesthesia Intensive Care (SFAR) French Group for Pediatric Intensive Care Emergencies (GFRUP) the French Dialysis Society (SFD)[END_REF], even though these guidelines were based on expert consensus at the time of publication. Randomized trials are not ethically possible in this specific situation as they would incur a major risk of death for patients. Outside of the emergency situations, however, a number of studies have been published in recent years. At the time when the questionnaire was sent out, 3 key studies investigating the optimal timing of nonurgent RRT initiation in the ICU had been published [START_REF] Gaudry | Initiation strategies for renal-replacement therapy in the intensive care unit[END_REF][START_REF] Zarbock | Effect of early vs delayed initiation of renal replacement therapy on mortality in critically Ill patients with acute kidney injury: the ELAIN randomized clinical trial[END_REF][START_REF] Barbar | Timing of renal-replacement therapy in patients with acute kidney injury and sepsis[END_REF]. These publications came after the development of the French guidelines, and thus, could not be included in them. Even more recently, a meta-analysis [START_REF] Gaudry | Delayed versus early initiation of renal replacement therapy for severe acute kidney injury: a systematic review and individual patient data meta-analysis of randomised clinical trials[END_REF] and a large international study including 3,019 patients corroborated previous results regarding the lack of difference in mortality according to the time when RRT was initiated in patients with AKI [START_REF]STARRT-AKI Investigators[END_REF]. The study by Zarbock et al. [START_REF] Zarbock | Effect of early vs delayed initiation of renal replacement therapy on mortality in critically Ill patients with acute kidney injury: the ELAIN randomized clinical trial[END_REF] is an exception, in that they demonstrated a significant reduction in mortality in the early-initiation group, but there was some debate regarding the study population (post-cardiac surgery), and the theoretical indication for RRT due to signs of pulmonary congestion.

The results of this survey of practices regarding the criteria for initiating RRT are in line with published data, notably in case of urea >40 mmol/L (51% agreed) or >50 mmol/L (77% agreed), and oliguria >72 h (40% agreed) and anuria >72 h (72% agreed). Older surveys of practices reported a stronger tendency of ICU physicians in both Europe [START_REF] Legrand | Management of renal replacement therapy in ICU patients: an international survey[END_REF] and the United States [START_REF] Thakar | Timing of dialysis initiation in AKI in ICU: international survey[END_REF] to initiate RRT earlier. This position was undoubtedly influenced by several metaanalyses whose publication now dates from around 10 years ago [START_REF] Seabra | Timing of renal replacement therapy initiation in acute renal failure: a meta-analysis[END_REF][START_REF] Karvellas | A comparison of early versus late initiation of renal replacement therapy in critically ill patients with acute kidney injury: a systematic review and meta-analysis[END_REF][START_REF] Wang | Timing of initiation of renal replacement therapy in acute kidney injury: a systematic review and meta-analysis[END_REF]. The ongoing AKIKI 2 study [START_REF] Gaudry | The artificial kidney initiation in kidney injury 2 (AKIKI2): study protocol for a randomized controlled trial[END_REF] is evaluating a strategy of RRT initiation at KDIGO stage 3 with urea>40 mmol/L or oligo-anuria >72 h at the time of randomization, with an early arm (RRT <6 h) and a deferred arm (urea >50 mmol/L). The results of this trial will undoubtedly provide novel evidence regarding the ideal time to initiate RRT for AKI in the ICU. Other studies are also in the pipeline regarding the use of predictive models to personalize RRT prescription in patients with KDIGO stage 3 AKI hospitalized in the ICU.

The presence of septic shock does not appear to be retained as an indication for RRT in our survey (with only 16% in agreement and 23% neutral). This is contrary to the hypotheses advanced several years ago, notably in animal models [START_REF] Staubach | Can hemofiltration increase survival time in acute endotoxemiaa porcine shock model[END_REF][START_REF] Rimmele | High-volume haemofiltration with a new haemofiltration membrane having enhanced adsorption properties in septic pigs[END_REF] regarding the interest of maintaining "inflammatory homeostasis," likely in the absence of an efficacious immunomodulating agent. Studies performed in the last 10 years have confirmed that there is no benefit, and it may even be harmful [START_REF] Payen | Impact of continuous venovenous hemofiltration on organ failure during the early phase of severe sepsis: a randomized controlled trial[END_REF] to initiate RRT in the aim of removing mediators of inflammation to improve patient prognosis in the ICU [START_REF] Honoré | Highvolume versus standard-volume haemofiltration for septic shock patients with acute kidney injury (IVOIRE study): a multicentre randomized controlled trial[END_REF][START_REF] Quenot | Very high volume hemofiltration with the Cascade system in septic shock patients[END_REF]. Multi-organ failure was reported by 37.5% of our respondents to be an indication for RRT, no doubt due to the severe metabolic disturbances it precipitates.

Regarding the choice of RRT technique (continuous vs. intermittent), this survey reveals a preference for continuous RRT, notably for fluid management, according to the Department Chiefs (73% in agreement), as it induces less hypotension than intermittent RRT (59% in agreement). French guidelines [START_REF] Vinsonneau | Renal replacement therapy in adult and pediatric intensive care: recommendations by an expert panel from the French Intensive Care Society (SRLF) with the French Society of Anesthesia Intensive Care (SFAR) French Group for Pediatric Intensive Care Emergencies (GFRUP) the French Dialysis Society (SFD)[END_REF] and literature data [START_REF] Vinsonneau | Continuous venovenous haemodiafiltration versus intermittent haemodialysis for acute renal failure in patients with multiple-organ dysfunction syndrome: a multicentre randomised trial[END_REF][START_REF] Rabindranath | Intermittent versus continuous renal replacement therapy for acute renal failure in adults[END_REF][START_REF] Bagshaw | Continuous versus intermittent renal replacement therapy for critically ill patients with acute kidney injury: a meta-analysis[END_REF] do not make it possible to draw any conclusion regarding the superiority of either technique and suggest in fact that the technique that is available and in which the staff are most competent should be used. Further, data are conflicting regarding renal function recovery according to the technique used [START_REF] Bell | Continuous renal replacement therapy is associated with less chronic renal failure than intermittent haemodialysis after acute renal failure[END_REF][START_REF] Schneider | Choice of renal replacement therapy modality and dialysis dependence after acute kidney injury: a systematic review and meta-analysis[END_REF], although new evidence has emerged from recent studies on the timing of RRT initiation showing no difference in recovery of renal function (although data were from secondary endpoints in those studies) [START_REF] Gaudry | Initiation strategies for renal-replacement therapy in the intensive care unit[END_REF][START_REF] Zarbock | Effect of early vs delayed initiation of renal replacement therapy on mortality in critically Ill patients with acute kidney injury: the ELAIN randomized clinical trial[END_REF][START_REF] Barbar | Timing of renal-replacement therapy in patients with acute kidney injury and sepsis[END_REF][START_REF]STARRT-AKI Investigators[END_REF].

The results of our survey are in line with French guidelines regarding the dose of dialysis and the modalities of its implementation, be it for intermittent or for continuous RRT. This is likely because the data in the literature are sufficiently robust to be adopted without question by prescribers [START_REF] Schiffl | Daily hemodialysis and the outcome of acute renal failure[END_REF][START_REF] Va/Nih Acute | Intensity of renal support in critically ill patients with acute kidney injury[END_REF][START_REF] Faulhaber-Walter | The Hannover dialysis outcome study: comparison of standard versus intensified extended dialysis for treatment of patients with acute kidney injury in the intensive care unit[END_REF][START_REF] Investigators | Intensity of continuous renal-replacement therapy in critically ill patients[END_REF]. Of note, typical CRRT doses were reported to be 25-35 mL/kg/h despite recommendations that they be in range of 20-25 mL/kg/h based on the ATN and RENAL trials [START_REF] Va/Nih Acute | Intensity of renal support in critically ill patients with acute kidney injury[END_REF][START_REF] Investigators | Intensity of continuous renal-replacement therapy in critically ill patients[END_REF]. It is likely that physicians prescribed a slightly higher dose in order to be sure that the actual dose delivered would be 20-25, when one takes into account potential interruptions over 24 h. Regarding the site of RRT catheter insertion, and the use of echographic guidance, the responses to our survey are also in conformity with national guidelines [START_REF] Vinsonneau | Renal replacement therapy in adult and pediatric intensive care: recommendations by an expert panel from the French Intensive Care Society (SRLF) with the French Society of Anesthesia Intensive Care (SFAR) French Group for Pediatric Intensive Care Emergencies (GFRUP) the French Dialysis Society (SFD)[END_REF], and probably also common sense, taking into account the patient's morphology and the risk of local infection [START_REF] Parienti | Femoral vs jugular venous catheterization and risk of nosocomial events in adults requiring acute renal replacement therapy: a randomized controlled trial[END_REF]. High-permeability membranes should be used for continuous RRT and in intermittent RRT (if ultrapure dialysate) [START_REF] Vinsonneau | Renal replacement therapy in adult and pediatric intensive care: recommendations by an expert panel from the French Intensive Care Society (SRLF) with the French Society of Anesthesia Intensive Care (SFAR) French Group for Pediatric Intensive Care Emergencies (GFRUP) the French Dialysis Society (SFD)[END_REF] and were reported to be the case for around 3-quarters of the Department Chiefs who responded. According to encouraging results in ICUs and in hemodialysis patients with tunneled dialysis catheters [START_REF] Hermite | Sodium citrate versus saline catheter locks for non-tunneled hemodialysis central venous catheters in critically ill adults: a randomized controlled trial[END_REF][START_REF] Parienti | Quasiexperimental study of sodium citrate locks and the risk of acute hemodialysis catheter infection among critically ill patients[END_REF], the use of citrate as a catheter lock for RRT catheters seems to be preferred in our study (53% in agreement), despite a recent study [START_REF] Quenot | Trisodium citrate 4% versus heparin as a catheter lock for nontunneled hemodialysis catheters in critically ill patients: a multicenter, randomized clinical trial[END_REF] and guidelines [START_REF] Vinsonneau | Renal replacement therapy in adult and pediatric intensive care: recommendations by an expert panel from the French Intensive Care Society (SRLF) with the French Society of Anesthesia Intensive Care (SFAR) French Group for Pediatric Intensive Care Emergencies (GFRUP) the French Dialysis Society (SFD)[END_REF] that preclude any firm conclusion about the best catheter lock to use (isotonic saline solution, ethanol, heparin, citrate, and taurolidine). Heparin remains the only catheter lock with marketing authorization at present, despite the absence of any benefit on catheter survival, and the existence of doubts regarding its innocuousness [START_REF] Bovet | Evaluation of anti-Xa activity after injection of a heparin lock for dialysis catheters in intensive care: a prospective observational study[END_REF].

Regional anticoagulation with citrate in continuous RRT is predominantly preferred according to our respondents, which is congruent with French commendations [START_REF] Vinsonneau | Renal replacement therapy in adult and pediatric intensive care: recommendations by an expert panel from the French Intensive Care Society (SRLF) with the French Society of Anesthesia Intensive Care (SFAR) French Group for Pediatric Intensive Care Emergencies (GFRUP) the French Dialysis Society (SFD)[END_REF], in patients with both high and low hemorrhagic risks. In those at low bleeding risk, filter duration is longer, in line with some publications in the literature [START_REF] Hetzel | Regional citrate versus systemic heparin for anticoagulation in critically ill patients on continuous venovenous haemofiltration: a prospective randomized multicentre trial[END_REF][START_REF] Wu | Regional citrate versus heparin anticoagulation for continuous renal replacement therapy: a meta-analysis of randomized controlled trials[END_REF][START_REF] Zhang | Efficacy and safety of regional citrate anticoagulation in critically ill patients undergoing continuous renal replacement therapy[END_REF]. This survey also shows that there remains considerable margin for improvement of practices in terms of training for ICU staff (physicians and nurses) and in terms of the development and implementation of standard operating procedures, which are recommended by French guidelines [START_REF] Vinsonneau | Renal replacement therapy in adult and pediatric intensive care: recommendations by an expert panel from the French Intensive Care Society (SRLF) with the French Society of Anesthesia Intensive Care (SFAR) French Group for Pediatric Intensive Care Emergencies (GFRUP) the French Dialysis Society (SFD)[END_REF]. The use of best practice has been shown to lead to a significant reduction in complications [START_REF] Schortgen | Hemodynamic tolerance of intermittent hemodialysis in critically ill patients: usefulness of practice guidelines[END_REF][START_REF] Graham | Nursing issues in renal replacement therapy: organization, manpower assessment, competency evaluation and quality improvement processes[END_REF].

Our study has several limitations. First, the number of participating ICUs is relatively low compared to the overall number in France. However, this level of response is classic in this type of study [START_REF] Beloucif | A European survey of the use of inhaled nitric oxide in the ICU. Working Group on Inhaled NO in the ICU of the European Society of Intensive Care Medicine[END_REF][START_REF] Cannesson | Hemodynamic monitoring and management in patients undergoing high risk surgery: a survey among North American and European anesthesiologists[END_REF] and our response rate is similar to that reported in another study on the same theme [START_REF] Legrand | Management of renal replacement therapy in ICU patients: an international survey[END_REF]. The dissemination of the questionnaire by the Department Chiefs among their ICU physicians was excellent (82% of responses), and completion rates were almost 100% on all questions. Second, the ICUs that answered the questionnaires may be those that are particularly highly motivated and interested in this topic, and therefore, results should be extrapolated with caution to other ICUs in France or abroad. Third, this was a survey of practices that aimed to record actual practices in ICUs, but there may be some potential for social desirability bias, whereby physicians may have answered what they thought would be the expected or "right" answer, especially since national guidelines exist for this topic [START_REF] Vinsonneau | Renal replacement therapy in adult and pediatric intensive care: recommendations by an expert panel from the French Intensive Care Society (SRLF) with the French Society of Anesthesia Intensive Care (SFAR) French Group for Pediatric Intensive Care Emergencies (GFRUP) the French Dialysis Society (SFD)[END_REF]. For this reason, a further study is ongoing on the ground to compare the results of this survey of practices to actual practices in ICUs across France. Finally, the Likert scales for response to the questions do not allow for detailed granularity in the responses but reveal mainly trends at a given time. It would likely be necessary to update the guidelines in light of recent evidence and to repeat this survey in the future to more accurately evaluate the translation of knowledge into practice at the bedside.

Conclusion

In summary, our study shows a satisfactory level of compliance with French guidelines and recent scientific evidence regarding initiation of RRT for AKI in the ICU. However, these self-declared results warrant confirmation by future observational studies of actual practices.

Acknowledgments

The authors thank Fiona Ecarnot, PhD (EA3920, University Hospital Besancon, France) for translation and editorial assistance. We are also grateful to all the physicians for their participation. We also thank David Attaf, Fabien Berthy, and Laure Cornillac (Fresenius) for their assistance in preparing the survey online.

Funding Sources

This study received no extramural funding.

Author Contributions

Study conception and design were performed by J.-P.Q., C.S., and C.V. Acquisition and analysis of data were performed by J.-P.Q., I.A., J.-Y.L., K.K., S.J., D.D.C., J.D., J.M., E.R., E.J., T.G., R.R., J.D., B.S., J.B., S.D.B., C.S., and C.V. Interpretation of data was performed by J.-P.Q., C.S., and C.V. Drafting of the first draft of the manuscript was performed by J.-P.Q., C.S., and C.V. Final approval of the version submitted by J.-P.Q., I.A., J.-Y.L., K.K., S.J., D.D.C., J.D., J.M., E.R., E.J., T.G., R.R., J.D., B.S., J.B., S.D.B., C.S., and C.V.

Statement of Ethics

Since this study was a survey of practices and did not involve patients, the need for informed consent and ethics approval was waived according to French legislation. Consent to participate was assumed by the fact that physicians completed the survey.

Conflict of Interest Statement

The authors have no conflicts of interest to declare.


Élise Temple-Boyer
email: elise.temple@gmail.com

Cette école thématique était organisée à l'initiative du laboratoire Dynamiques sociales et recomposition des espaces (LADYSS, UMR 7533, CNRS). Elle s'inscrivait dans le cadre du projet CRIQUE1 (Risques et inégalités face à la gestion durable de la ressource hydraulique en Méditerranée occidentale), qui mobilise diverses équipes de recherche dans six pays méditerranéens (Algérie, Maroc, Tunisie, Espagne, Portugal et France). Si de nombreux travaux ont déjà été effectués sur la question de la gestion hydraulique dans les pays de la Méditerranée, peu ont porté sur la perception du risque lié à la pratique de l'irrigation agricole, dans sa dimension sociale locale. C'est sur cette question que se penche le projet CRIQUE, qui a également pour autre objectif d'entreprendre une évaluation critique des expériences menées dans les pays méditerranéens en matière de gestion participative des ressources en eau et de leur rôle dans la minimisation ou l'aggravation des risques liés à l'irrigation.

Cette école a réuni une quarantaine de chercheurs, certains confirmés, d'autres plus jeunes, venus des rives nord et sud de la Méditerranée, autour d'une vingtaine de communications qui ont abordé la question dans une démarche interdisciplinaire. Le programme prévoyait, outre la présentation par pays des travaux réalisés dans le cadre du projet, quatre ateliers centrés sur les thèmes suivants : la ressource hydraulique vue sous l'angle de la production du risque, les perceptions du risque chez les acteurs usagers et gestionnaires de l'eau, les dispositifs de gestion de l'eau (approches participatives et politiques publiques) et la démarche interdisciplinaire appliquée aux recherches sur les questions hydrauliques. Ce dernier thème, pourtant prometteur, n'a finalement pas été l'objet de discussions, mais l'interdisciplinarité n'était pas pour autant absente, surgissant au gré de ces journées à travers les postures et les travaux des chercheurs qui sont intervenus.

En introduction, Jean-Paul Billaud (sociologue, LA-DYSS) rappelle que la question de l'eau peut être envisagée sous l'angle du risque et sous celui de la dépendance réciproque entre les populations et leur environnement. En effet, la gestion de l'eau peut être considérée comme une gestion de risque, dans la mesure où les conventions qui en régissent les dispositifs ont pour finalité de réduire les aléas aussi bien naturels que techniques. La question de l'eau peut aussi être abordée sous l'angle de l'équité, les inégalités en matière d'accès à l'eau requérant des formes de gestion du risque très contrastées.

Le premier atelier comportait quatre communications. Dans les deux premières, deux paradoxes sont mis en évidence. Le premier l'est par Michel Drain (géographe, CNRS) à propos de l'Espagne. Il note que, malgré la grande diversité et le raffinement des techniques et des méthodes de lutte contre la sécheresse et malgré l'expérience ancienne du risque de pénurie qui existe dans ce pays, les politiques d'économie d'eau y ont échoué. Le deuxième est le fait bien connu, rappelé par Yamna Djellouli (géographe, Université du Maine), que les pays du Maghreb sont tout autant touchés par la rareté que par l'excès d'eau, signe de la forte inégalité spatiale de la répartition de la ressource. Les remèdes sont, d'une part, la solidarité nationale à travers les transferts interrégionaux, d'autre part, le recours aux eaux non conventionnelles (dessalement et recyclage des eaux usées). On peut toutefois se demander si ces alternatives sont des solutions durables.

Deux points de vue sont venus compléter ce premier cadrage. Se situant sur le plan technique, Haithem Bahri (agronome, Institut national des recherches en génie rural, eaux, forêts [INRGREF], Tunis) souligne que l'irrigation peut aussi être un instrument d'une gestion optimale et durable de la ressource, à condition d'être bien maîtrisée. Cette maîtrise passe par l'évaluation des impacts de l'irrigation sur l'environnement, à travers une approche systémique qui permettrait de réduire les risques de sécheresse, sans pour autant épuiser totalement la ressource. De son côté, Leila Chikhaoui (juriste, Faculté des sciences juridiques, économiques et de gestion [FSEJG], Jendouba, Tunisie) réintroduit la dimension sociale, en rappelant qu'une gestion durable des risques liés aux usages de l'eau passe nécessairement par une réduction des inégalités de l'accès à l'eau et par une plus grande justice sociale. Ce premier atelier était ainsi centré sur des constats de vulnérabilités sociales et d'inégalités vis-à-vis de la ressource.

Il ne suffit pas de prendre la mesure des risques induits par une situation de pénurie d'eau, il est aussi nécessaire de mieux évaluer la perception qu'en ont les acteurs : tel était précisément le second thème de ces journées. Curieusement, c'est là une préoccupation jusqu'à maintenant peu présente en France, observe Bernadette de Vanssay (psychosociologue, Université Paris V), qui note même que la notion de risque n'a pas été prise en compte lors du Grenelle de l'environnement. La perception actuelle du risque tire-t-elle profit de la mémoire historique ? C'est la question que se pose Sylvie Clarimont (géographe, Université de Pau et des Pays de l'Adour), à propos du risque d'inondation, dans une recherche sur le bassin de l'Adour, à travers le dépouillement d'archives départementales. Elle en conclut que c'est en fait moins une mémoire du risque qu'une mémoire de l'indemnisation que ces documents transmettent. Ces matériaux de recherche que sont les archives institutionnelles peuvent-ils transmettre une mémoire à proprement parler du risque ? La question est posée. Il semble de toute façon que les acteurs actuels de la gestion du risque s'approprient peu ce type de mémoire, voire ne s'y réfèrent absolument pas. Cela peut s'expliquer par son caractère composite, mais aussi par le caractère fluctuant des politiques de conservation et en raison d'une transmission défaillante de la mémoire institutionnelle longue. La mémoire collective est, elle aussi, déficiente, remarque Bernard Picon (sociologue, CNRS) à propos des récentes inondations survenues en Camargue. Dans cette région, la réalisation de grands aménagements hydrauliques contre les crues depuis le milieu du XIX e siècle a permis que s'installe un sentiment de sécurité qui a fait oublier le risque d'inondation. Cet exemple montre comment les techniques modernes et les représentations des « territoires de l'eau » qu'elles induisent peuvent devenir des facteurs aggravants de risque.

À l'appui de ces réflexions sur la perception de la gestion de l'eau et des risques, divers films ont été projetés, d'une part dans un contexte ibérique, d'autre part dans un contexte maghrébin. Les trois petits films, présentés par Fabienne Wateau (ethnologue, CNRS), sur divers objets traditionnels de mesure de l'eau d'irrigation (la canne à mesurer l'eau, la pierre de partage de l'eau, la conque), dans le Nord-Ouest du Portugal et le Sud de la Galice espagnole, invitaient à réfléchir sur la pertinence des choix techniques traditionnels en matière d'eau d'irrigation et sur la prégnance du social dans la distribution de l'eau. On peut, en effet, se demander si ces techniques sont réellement désuètes et si elles ne pourraient pas offrir une alternative aux techniques actuelles dans la réduction des vulnérabilités. Quant aux films de Hassen Kemmoun (agronome, École nationale d'agriculture [ENA], Meknès, Maroc), ils offraient une documentation sur quelques expériences modernes d'action collective dans le domaine de l'irrigation au Maroc et mettaient en valeur l'utilité de la vidéo pour aider les exploitants à mieux structurer leur raisonnement et leurs propositions. Ces films visaient à illustrer l'idée avancée par Marcel Kuper (hydrologue, Cirad) et Patrick Caron (géographe, Cirad) selon laquelle l'action collective permet à la petite agriculture familiale de s'adapter aux exigences des systèmes de grande hydraulique. Elle permet également une meilleure adaptation face aux marchés, aux réformes institutionnelles et à la rareté de l'eau.

Le troisième atelier abordait plus spécifiquement la question des modalités de gestion intégrée de l'eau. D'après Thierry Ruf (agroéconomiste, IRD), l'eau peut prendre, en même temps et dans un même territoire, des formes différentes en tant que bien économique. Tout dépend du statut de l'espace et du réseau dans lequel elle circule : elle peut être publique, privée, commune ou soumise à péage, chaque cas ayant ses propres bénéficiaires, ses propres exclus et ses propres crises dans la gestion de l'eau. L'analyse des évolutions actuelles des modes de gestion des ressources en Tunisie et au Maroc, présentée par Bruno Romagny (économiste, IRD), conduit à s'interroger sur les rôles complémentaires de l'État et des acteurs locaux. En effet, le devenir des institutions décentralisées « traditionnelles » ou « modernes » de gestion des ressources est très dépendant du jeu de concurrence entre un ensemble d'acteurs et de pouvoirs aux intérêts divergents. L'avenir des populations en découle. Cela peut conduire à un paradoxe de la participation : elle est invoquée et utilisée, au nom de l'intérêt des populations, pour mettre en pratique des mesures aux objectifs globaux qui, en fin de compte, peuvent desservir les intéressés.

La participation est plus facile à prôner qu'à pratiquer ! Audrey Richard-Ferroudji (sociologue, Cemagref) analyse les difficultés de mise en oeuvre des dispositifs de participation dans le cas du bassin versant de la Lentilla (Pyrénées-Orientales). Son analyse critique des outils de démocratie participative souligne les difficultés, soulevées par la participation, à accueillir et à composer avec une pluralité de valeurs, d'objectifs et d'attachements vis-à-vis de l'eau et de sa gestion2 . Elle montre que l'appropriation des outils de participation par les divers acteurs engagés dans la gestion de l'eau est une dynamique de déformation mutuelle et d'ajustement des choses et des personnes, et que cette appropriation dépend des valeurs à travers lesquelles l'individu maximise sa satisfaction3 .Enfin, s'appuyant sur l'exemple de la nappe de Beauce, Olivier Petit (économiste, Université d'Artois) observe que la pratique de gestion des ressources hydriques qui se veut intégrée n'en est encore qu'au stade de l'objectif. Cela est dû à une faible incitation économique en sa faveur, à la difficulté des contrôles réglementaires et au temps exigé par la mise en oeuvre des instruments participatifs.

En conclusion, ces journées ont montré que la gestion « participative » et la gestion « intégrée » de l'eau soulèvent encore, toutes deux, beaucoup de difficultés en raison d'une mise en oeuvre plus complexe qu'il n'y paraît dans le discours. La question de leur adoption systématique par les gestionnaires dans les actions visant à la réduction des risques reste posée. Les communications de ces journées ont fait l'objet d'une publication sur CD-ROM, disponible sur demande au LADYSS4 .

Ce projet a bénéficié du soutien financier du CNRS, de la Maison des sciences de l'homme (Paris) et de la Fédération de recherche CNRS Capitalisme(s) et Démocratie(s) (Paris X).

Cf. Richard-Ferroudji, A., 2008. L'Appropriation des dispositifs de gestion locale et participative de l'eau : composer avec une pluralité de valeurs, d'objectifs et d'attachements. Thèse de doctorat en sociologie, Paris, EHESS.

Pour conduire son analyse, A. Richard-Ferroudji introduit la notion de « niveaux de biens ». Elle en distingue trois : le bien-être physique, la satisfaction d'accomplir un objectif et la satisfaction de contribuer à ce qui est considéré comme un bien collectif.

S'adresser au secrétariat du LADYSS : béatrice.moellic@u-paris10.fr


domain: shs sde

text:
Christine Hatté

Christelle Lahaye

Michel Fontugne

Philippe Lanos

Antonio Pérez-Balarezo

Paulo Ramos

Eric Boëda

Early presence of Homo Sapiens in South America -a review of about 40 years of geochronological research in the Serra da Capivara National Park, Piauí, Brazil

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

Early presence of Homo Sapiens in South America -a review of about 40 years of geochronological research in the Serra da Capivara National Park, Piauí, Brazil Christine Hatté1,2 , Christelle Lahaye 3 , Michel Fontugne 1,4 , Philippe Lanos 3,5 , Antonio Pérez-Balarezo 6 , Marcos Paulo Ramos The settlement of the Americas, particularly the question of how early Homo Sapiens arrived in South America, is a central topic of scientific interest within the archaeological community. Growing evidence suggests an early human presence in the southern part of the American continent, and some previously overlooked findings are now being brought to light and acknowledged. The dating associated with evidence of human presence, regardless of the method used, suggests that humans might have been present 30, 40 or even 50 kyr BP. Among various archeological sites, significant efforts have been dedicated to the region of Serra da Capivara in Piauí, Brazil, for both archaeology and dating, for several decades, since the initial investigations conducted by Niède Guidon and Georgette Delibrias 1 in 1980s. In this communication, we present a comprehensive analysis of the dating results obtained over the past twenty years, within the framework of systematic characterization of all stratigraphical and/or archeological units. Geochronological modeling is carried out with the ChronoModel software 2 , in particular by using its specific option that allows for the correlation of multiple constraints among datings, events, and units. This feature enables us to link geochronological events by their significance, stratigraphic succession, and their association to the same technical facies, as defined by meticulous and objective analysis of lithic assemblages. With the help of these multiple constraints, we can objectively determine the techno-cultural phases by their boundaries (both start and end) and duration, each associated with a probability distribution. The meta-analysis of over a hundred 14 C and OSL datings, which characterize more than 50 archeological layers across eight sites in and around the Serra da Capivara National Park, indicates a nearly continuous human presence over the last 40,000 years. Furthermore, it shows varying occupation of these sites depending on the period and their geographical location. This work is part of the ANR SESAME project (ANR-20-CE03-0005) and of MEAE Piaui archeological mission. The data collection from the LSCE 14 C research laboratory made it possible.

  Rennes, UMR 6118 CNRS Université de Rennes, Campus scientifique de Beaulieu, CS 74205, Rennes, France 6-ArScAn, UMR 7041 CNRS Université Paris Nanterre, Nanterre, France 7-PPGArq-Museu Nacional, Universidade Fedreal do Rio de Janeiro, Rio de Janeiro, Brazil

	7 , Eric Boëda 6
	1-Laboratoire des Sciences du Climat et de l'Environnement, UMR8212 CEA CNRS UVSQ, Université
	Paris-Saclay, Gif-sur-Yvette, France
	2-Division of Geochronology and Environmental Isotopes, Institute of Physics, Silesian University of
	Technology, Gliwice, Poland
	3-Archéosciences Bordeaux, UMR 6034 CNRS Université Bordeaux-Montaigne, Maison de
	l'archéologie, Université Bordeaux-Montaigne, Pessac, France
	4-currently at LAMPEA, UMR 7269 CNRS Aix Marseille University Ministère de la Culture, LAMPEA,
	Aix-en-Provence, France
	5-Géosciences-

Guidon N. and Delibrias G. (1986) Carbon 14 dates point to man in the Americas 32,000 years ago. Nature 321, 769-771.

https://chronomodel.com/ -Lanos P. and Dufresne P. (2019) ChronoModel version 2.0: Software for Chronological Modelling of Archaeological Data using Bayesian Statistics, version 2.0.