Fabio Ardiani
email: fardiani@enit.fr

Martin Mujica

Mourad Benoussaad

Alexandre Janot

Jean-Yves Fourquet

MESSII: a parameter identification dataset for KUKA IIWA collaborative manipulator

Keywords: Data-Set, Identification, Collaborative Robotics

In this paper, we present the MESSII Dataset (Manipulator Experimental SyStem Identification and Interaction Dataset). This novel dataset aims at providing numerous sequences of movements of the KUKA iiwa manipulator, in order to evaluate methods for identification and estimation of the robot's dynamic parameters and signals, respectively. Different movements of the manipulator are provided, including trajectories moving one or multiple joints at the same time, trajectories that are specially designed for parameter identification, and trajectories including a payload attached at the end-effector of the manipulator. The information obtained from the propioceptive sensors of position and torque is presented. Furthermore, as physical Human-Robot Interaction (pHRI) is the main application of this robot, sequences with interaction with a person are provided to estimate the forces applied, where a force-torque sensor acts as the ground truth. The dataset can also be used in ROS to evaluate real-time methods as information is presented in rosbags files. Possible applications are given, highlighting the advantage of the dataset to help with state-of-the-art challenges, without the need of the real robot nor doing new and complex experiments. The dataset, as well as more information and tools, are publicly available in https://messii-dataset.enit.fr.

Introduction

Physical human-robot collaboration is a growing area in robotics, where the robot and the human do not only share their work-space, but they also share objectives and tasks [START_REF] Santis | An atlas of physical human-robot interaction[END_REF]; [START_REF] Ajoudani | Progress and prospects of the humanrobot collaboration[END_REF]). The fact that a human can interact in an unpredictable way with the robot, brings up new challenges in terms of control and design. These involve not only the analysis of the task performance and the manipulator's integrity, but also of the human safety [START_REF] De Luca | Collision detection and safe reaction with the dlr-iii lightweight manipulator arm[END_REF]; [START_REF] Haddadin | Requirements for safe robots: Measurements, analysis and new insights[END_REF]). For this, besides a new generation of well-performing robotic manipulators and rich proprioception sensing [START_REF] Albu-Schäffer | The dlr lightweight robot: design and control concepts for robots in human environments[END_REF]), a suitable control has to be designed, which is usually of the model-based type [START_REF] Siciliano | Robotics: modelling, planning and control[END_REF]). The more the model approaches reality, the simpler will be to design the controller to interact with the human in a compliant and human-friendly way.

Dynamic equations of cobots have been widely studied in literature [START_REF] Khalil | Modeling identification and control of robots[END_REF]) which relate signals as the torque, position, velocity and acceleration of joints between each other and also with dynamic parameters as the inertia, mass and center of mass coordinates of the links. The signals can be measured by choosing a correct set of sensors, whereas there are three main methods to obtain the numerical value of the dynamic parameters: physical experiments carried out on the manipulator's individual parts, CAD techniques and dynamic parameter identification methods. The fact that for carrying physical experiments, each link needs to be isolated from the others, thus the manipulator needs to be disassembled, makes this option non-viable most of the times. Moreover, most available collaborative robots in the market are usually not intended for research, and manufacturers do not provide crucial information like its CAD model and related parameters. Because of these reasons, in general, the only feasible option is dynamic parameter identification.

In order to achieve this purpose, there is a large amount of parameter identification methods available in literature (see the survey in [START_REF] Leboutet | Inertial parameter identification in robotics: A survey[END_REF]). Moreover, several works on dynamic parameter identification of industrial collaborative manipulators can be found in bibliography as the ones on the: KUKA iiwa [START_REF] Stürz | Parameter identification of the kuka lbr iiwa robot including constraints on physical feasibility[END_REF]), KUKA LWR4+ [START_REF] Jubien | Dynamic identification of the kuka lwr robot using motor torques and joint torque sensors data[END_REF]), Franka Panda Emika [START_REF] Gaz | Dynamic identification of the franka emika panda robot with retrieval of feasible parameters using penalty-based optimization[END_REF]), ABB IRB14000 (YuMi) [START_REF] Taghbalout | Experimental dynamic identification of a yumi collaborative robot[END_REF]), UR3 and UR5 [START_REF] Raviola | Effects of temperature and mounting configuration on the dynamic parameters identification of industrial robots[END_REF]).

The process of parameter identification consists of several steps comprising the modeling, the generation and execution of enough exciting trajectories, the data processing, the parameter estimation itself and the results evaluation (for more information about system identification refer to [START_REF] Ljung | System identification[END_REF]). This task can be time consuming, being usually a try and error exercise. In addition to this, the manipulator may be unavailable, e.g. it is being used to perform other tasks or it is located in a place where it cannot move freely. One solution could be to design a simulation in order to test methods and algorithms. However, simulated data will always be a simplification of reality, where unmodeled effects both in the deterministic (dynamic effect) and stochastic (noise) parts are present.

In other disciplines, the solution to these issues has been found in shared datasets. They are a positive product of the advent of big-data and open science. They are a way to give the research community and society in general the tools to both: verify publications based on the dataset either because it may have experiments that are difficult, tedious, or impossible to replicate, and also give the possibility to fellow multidisciplinary researchers to continue the research work and deepen the knowledge on one topic from different points of views. This is why there are some datasets that have become quite famous as [START_REF] Geiger | Vision meets robotics: The kitti dataset[END_REF] and [START_REF] Sturm | A benchmark for the evaluation of rgb-d slam systems[END_REF].

The aim of this work is to present a complete and consistent data-set of the collaborative 7-dof KUKA iiwa 14 R820 manipulator which allows the scientific community to try state-of-the-art and new algorithms throughout the steps of the identification process in different scenarios without the need of a physical robot. Classical and collaborative scenarios that allow the identification of the manipulator, load and interaction parameters are considered.

The paper is structured as follows: first, a state-of-the-art review of other dataset using robotic manipulators is done. Second, we present the robotic platform used, including the robot, the payload, the sensor and the computer. Then, the new MESSII dataset is presented: its structure, the available data and how it was obtained. After that, some applications and challenges are shown. Finally, conclusions are made.

Related Work

In the area of robotic manipulators, there are several datasets dealing with the problem of grasping and manipulation of objects (for an extensive survey see [START_REF] Huang | Recent data sets on object manipulation: A survey[END_REF]). Most of them are datasets containing information of activities humans carried out in order to make the robots learn from them. De la [START_REF] De La Torre | Guide to the carnegie mellon university multimodal activity (cmu-mmac) database[END_REF] collects multimodal data of human behavior in a cooking task using RGB cameras, accelerometers placed on the human, microphones, and motion capture system. [START_REF] Mandery | The kit whole-body human motion database[END_REF] presents a whole-body human motion database consisting of captured motion data from the human and objects being manipulated using a marker-based motion capture system. [START_REF] Maurice | Human movement and ergonomics: An industry-oriented dataset for collaborative robotics[END_REF] records persons carrying out industrial activities for an ergonomic study using optical motion capture, inertial motion capture (IMUS placed on the body), hand contact and finger flexion sensors, and video cameras. [START_REF] Pirsiavash | Detecting activities of daily living in first-person camera views[END_REF] present a database with first-person camera views of daily living activities. [START_REF] Roggen | Collecting complex activity datasets in highly rich networked sensor environments[END_REF] places a large amount of sensors in an environment in order to carry out machine recognition on human activities.

These are just some of the huge amount of datasets available which are mainly focused on the study of the human movement in order to develop image-recognition and machine-learning algorithms, which could be subsequently used to teach a robot how to behave in different situations. On the other side, there are some datasets that focus on the behavior of robots. [START_REF] Gao | Jhu-isi gesture and skill assessment working set (jigsaws): A surgical activity dataset for human motion modeling[END_REF] is a surgical activity dataset for human motion modeling, captured using the Da Vinci surgical system and eight surgeons performing different tasks. Although it is a tele-operated system, it presents kinematic data from the robot (Cartesian positions, orientations, velocities and gripper angle) and stereo video data captured from the endoscopic camera. [START_REF] Dasari | Robonet: Large-scale multirobot learning[END_REF] introduces a huge dataset of videos of different manipulators carrying out different trajectories. [START_REF] Levine | Learning hand-eye coordination for robotic grasping with deep learning and large-scale data collection[END_REF] introduces a dataset of pushing and grasping motions for self-supervised learning objectives using the KUKA IIWA manipulator. To the authors knowledge, it represents the only dataset where, besides position measurements and camera's images, measurements of torque from propioceptive sensors are also available.

Most of these publications deal with the problem of behavior learning for robots based on video information. However, as far as the authors are concerned, there is no dataset focused on dealing with measurements of propioceptive sensors of collaborative manipulators and interaction forces from external sensors, in order to carry out dynamic parameter identification and to estimate human contact. These are tasks that are needed in almost every implementation of a collaborative manipulator, thus its utilization becomes essential for robotics.

Robotic Platform

The KUKA IIWA manipulator

The MESSII Dataset has been collected using the industrial robot KUKA LBR iiwa 14 R820 * shown in Figure 1. It is a 7-dof lightweight robotic manipulator intended for collaborative applications [START_REF] Albu-Schäffer | The dlr lightweight robot: design and control concepts for robots in human environments[END_REF]). Similarly to other collaborative robots, it is equipped with both: encoders to sense the joint/link positions and torque sensors to measure the link-side torque at a rate of up to 1000 Hz. The robot is also equipped in its tip with the interface Media Flange Touch Electrical from KUKA.

The collaborative manipulator's structure is depicted in Figure 2. There are five signals that the KUKA iiwa controller makes available for users:

• Commanded Position: After processing the desired points/trajectory that the user introduced, the controller calculates this signal. It is the position of the successive points that the robot is asked to follow, which means the reference trajectory. • Commanded Torque: It is the torque related to the commanded position by the internal dynamic model that is used by the controller. • Sensed Position: It is the measurement of the linkside position. It is either a real measurement or an estimation made by the manufacturer from sensing the motor position and knowing the gearbox parameters.

• Sensed Torque: It is the measurement of the torque sensor placed after the gearbox, typical of collaborative manipulators (Albu-Schäffer et al. ( 2007)). • External Torque: It is a filtered signal product of the difference between the commanded torque and the sensed torque. It accounts for all phenomena that the model of the controller does not take into consideration. The Force-Torque Sensor

In order to enhance the platform for some set of experiments, a force-torque sensor was equipped on the tip of the robot.

The capacitive 6-axis force torque sensor, model RFT76-HA01 from ROBOTOUS † was used. It can provide the measurements of forces in the three directions (with a limit of 300 N and a resolution of 200mN for each axis) and the three components of torque related to each axis (with a limit of 10 Nm and a resolution of 8 mNm for each axis) at a rate of up to 1000 Hz. Weighting 200 g, it is powered by an EtherCAT adapter that uses CAN interface to communicate with the sensor. It was installed on the tip of the robot via a 3D printed coupling. The whole setup can be seen in Figure 1.

The Load

The load is a steel cylinder of 34 mm of height and 140 mm of diameter. It weights 4.012 kg (4.092 kg when adding screws), and taking into account its regular shape, its center of mass is considered to be in the geometrical middle point.

The inertia tensor can be approximated with a diagonal matrix of inertia 0,01 kg.m 2 along the principal axis, and 0,0054 kg.m 2 along the other two axis.

When attaching it to the manipulator (see Figure 1), approximated parameters were indicated by the user to the controller which will have an influence on the Commanded and External signals. Therefore, we will have 4.1 kg, 0.01 kg.m 2 for all three inertias, and with the center of mass centered around the z axis and displaced 22 mm in the z direction.

The Computer

The data of both, the robot and the sensor, were logged at a rate of 1000 Hz on an external computer. We used a HP ZBook 15 G2 Mobile Workstation ‡ (Intel Core i7-4710MQ 2.5 GHz, 2.50 GHz, 8 Go DDR3L SDRAM) running Ubuntu 18.04.5 LTS. The communication with both the KUKA iiwa controller and the sensor is done via C/C++ client applications communicating in real time. In the case of the manipulator, it was performed using the Fast Robot Interface (a version presented in Schreiber et al. ( 2010)), which is an open-source library for remote control of some KUKA robots.

Figure 3 shows a diagram on how all the parts of the framework interact and exchange information between each other.

The Dataset

Structure

The dataset is structured as presented in Figure 4. The three main folders (Standalone, ROS and RAW) contain the same sub-folder tree. Hence, each of these three folders contains the four sub-folders corresponding to the possible application, either for the identification of the robot, the sensor, the load or for pHRI. The Standalone and ROS folders present the data gathered and processed (filtered). The only difference is that Standalone presents data in several .log files, whilst ROS presents the information in rosbags. The RAW folder presents the non-processed data.

The sub-folders description for each of the four possible applications can be seen in Figure 5. Challenges -Parameter Identification. Similarly, for load identification, we provide global and individual trajectories. As for the sensor identification, we provide individual trajectories. Whether the trajectories are global or individual, we provide several examples with variations of the type of trajectory or the posture of the robot while performing the movement. Finally, for the case of pHRI, we provide two types of interactions with the environment (a person). First, the interaction appears exclusively at the end-effector level (i.e. forces captured by the F/T sensor) and the second case contains interactions at different points of the kinematic chain of the robot. For both of these cases, we provide sequences where the interactions happen while the robot is moving (under Impedance Control) and when the robot is in a static condition.

Data Collection Trajectories

The dataset is composed of two types of trajectories. The so-called global trajectories where all the joints move at the same time, and the individual or sequential trajectories where just one joint moves. Design of an exciting enough trajectories is an area of identification by itself and has attracted a lot of attention [START_REF] Pukelsheim | Optimal design of experiments[END_REF]). It can be summarized in a non-linear optimization problem of the condition number of the regression matrix of the dynamic model, with multiple linear and non-linear constraints. This stage is already provided in the dataset, and in this section a brief explanation of each of the trajectories will be given.

On the one hand, there are three types of global trajectories present in the dataset: PTP, SPL and DS. The first two are obtained from the PTP (point-to-point) and SPL (spline) motions that the KUKA controller provides. 50 points are randomly selected inside the manipulator's reachable workspace, and then the corresponding interpolation is done by the controller. This way of designing trajectories has proven to be enough for identification in [START_REF] Jubien | Dynamic identification of the kuka lwr robot using motor torques and joint torque sensors data[END_REF]. based on finite Fourier series presented in [START_REF] Swevers | Optimal robot excitation and identification[END_REF] was used. A 5th order sum of harmonics was chosen, and constraints regarding position and velocity limits, zero initial joint position, velocity and acceleration were considered in the optimization problem.

On the other hand, three type of sequential trajectories were carried out. First, a trajectory pretended for friction identification was designed using PTP motion, in which the joint in study moves from one point to another at constant different speeds. In this way, the inertial effects are reduced. Contrary, another trajectory was designed, also by means of a PTP motion, for inertial parameters identification in which the intervals where the joint is accelerating or decelerating are more significant than those of constant velocity. Finally, a trajectory from a finite Fourier series, as the one explained in the previous paragraph, is designed using the DirectServo motion.

Synchronization

The computer has two parallel processes, as shown in Figure 3. The main one is in charge of saving the information coming from the manipulator's controller at a rate of 1000 Hz with its respective timestamp. The second process saves the information of the force-torque sensor on a shared memory also at 1000 Hz, which the main process then reads and saves on the corresponding file. This method will ensure that all the data is time-stamped and well-synchronized by having a maximum shift between the measurements of the manipulator and those of the external sensor of 1ms in the worst-case scenario.

Data Processing

Filtering Besides the raw measurements, filtered data is available to facilitate the work for users who want to test directly the identification methods avoiding the signal digital processing. The proposed filtering is a simple 4-steps process inspired in the work of [START_REF] Gautier | A new closedloop output error method for parameter identification of robot dynamics[END_REF]. First, the raw data is filtered via a non causal zero-phase digital Butterworth filter of order 2 with cut-off frequency at 3.5 Hz, both, in the forward and reverse direction to avoid lag. Second, a numerical central differentiation is made to obtain the speed and acceleration signals from the filtered position. Third, a downsample of order 20 is made to obtain an overall signal of 50 Hz and reduce computational burden. Finally, border effects are deleted, as well as all those points where the joints in study have a velocity lower than 0.05 rad/s (except for the trajectories with human interaction). This is done to avoid problems due to the usually used non-smooth around 0 velocity model of friction including just the Coulomb and viscous friction effects.

Rosbags

To allow the use of the dataset with ROS, the same information of the Standalone version is provided by several rosbags. The main advantage of the rosbag version of the dataset is that it can be used with other predefined nodes as well as in real-time applications. For instance, real-time identification of the robot's parameters or force observers can be implemented and tested.

The information presented in the standalone version is replicated in the rosbags. The structure as mentioned is the same, but instead of having several files for each experiment, they are all gathered in a single rosbag. Each rosbag contains the following topics :

• FT sensor : Containing the three forces and three torques as a wrench vector of the type geometry msgs/WrenchStamped. • jointCommanded: Containing the commanded states (position, velocity and torque) for the seven joints as a sensor msgs/JointState type of message. • jointMeasured: Containing the measured states (position, velocity and torque) for the seven joints as a sensor msgs/JointState type of message. • jointExternal: Containing the external states (position, velocity and torque) for the seven joints as a sensor msgs/JointState type of message.

Details on how to run the rosbags, listen to the available topics and create new rosgabs are included as tools in the dataset web.

Calibration

As the recorded measurements from the KUKA iiwa manipulator are from propioceptive sensors and in the jointspace, no external calibration needs to be done. However, the robot comes with a load determination tool, which will have a direct effect on the calculation of the commanded signals and external torque. In this work, the load in the controller was set to zero for the trajectories without load, with the sensor and with human interaction. For the trajectories where the load is placed, the estimated values were already described. This means that, in some experiments, the external torque will have just the contribution of friction and uncertainties of the model that is used by KUKA to control the robot, while in others, it will also include the effect of the sensor's weight, paylod's uncertainties and the possible human-robot interaction.

Furthermore, the sensor is well-aligned to the axis of the Media Flange thanks to the "location pins" and the way the coupling was designed (see CAD model present in the dataset web). As for the sensor calibration, each trajectory done in the pHRI part begins with a few seconds of the robot in static condition and with no interactions. This, combined with the identification of the after-sensor dynamic, should allow to recover the forces coming exclusively from the interactions.

Finally, camera recordings are also included to visually depict the interactions with the person in the respective pHRI tests.

Application and Challenges

Parameter Identification

The parameter identification procedure can be summarized in the seven steps shown in Figure 6. It is an iterative procedure which will ultimately depend on the application of the obtained model and its expected performance. These tasks can be time consuming, thus, being able to test the whole procedure before executing it on a specific manipulator can be of advantage to users. This is the reason why this dataset facilitates steps 3, 4 and 5 of the procedure, allowing users to test their own overall solution on real data without the need to own and code a manipulator.

Each of the steps can be solved in several ways, presenting interesting issues and challenges, and some of them will be briefly mentioned. First, in collaborative robotics there are still some questions regarding which is the best way to model the joint flexibility, payloads and friction [START_REF] Luca | Feedforward/feedback laws for the control of flexible robots[END_REF]; Van Geffen (2009); [START_REF] Raviola | Effects of temperature and mounting configuration on the dynamic parameters identification of industrial robots[END_REF]). This dataset allows the user to test and compare different models. For instance, the explicit dynamics, the energy or the power methods can be used to derive the model, and analytical closed-form rules or numerical tools as the QR and SVD decomposition can be used to obtain the reduced model.

Furthermore, although we propose filtered data, ready to be used on identification methods, we also provide the raw information, to let users apply their own filtering stages. Digital signal processing textbooks address this issue extensively (Anderson and Moore ( 2012)), and even though this stage will usually strongly depend on the application, being able to test the whole data processing step on real data can be useful.

In addition, the proposed dataset allows the user to test different parameter identification methods (step 6 in Figure 6). The selected method can range from a simple en-bloc method of a system linear with respect to the parameters, such as the Least-Squares solution, to neural networks and complex recursive solutions that could be applied online. This last topic is of much interest, as manipulators working on unpredictably changing environments require an online evaluation in order to estimate interactions and detect faults and collisions. The identification can be done in a global form, meaning that all parameters are estimated at the same time, or sequentially, where parameters are excited at different moments. Furthermore, the identification methods can include physically feasibility constraints to obtain parameters which are congruent with reality, which is a topic that brings a lot of attention lately [START_REF] Sousa | Physical feasibility of robot base inertial parameter identification: A linear matrix inequality approach[END_REF]; Janot and Wensing ( 2021)). Moreover, the provided signals also allow the identification of the model that is included in the controller, and by means of black-box identification methods, the structure of the controller. This enlarges widely the application and utility of the dataset, as many aspects of system identification can be addressed.

Finally, different techniques of model validation can be tested and new ones can be proposed depending on the desired application, e.g. tools can be used as analysis of residuals, analysis of estimates and analysis of model fit [START_REF] Ljung | System identification[END_REF]). Application example. In order to show the utility of the dataset and emphasize one of the mentioned challenges, we have carried out a simple Least-Squares identification of the parameters of joint 4 using the Sequential Joint 4 Inertia Filtered trajectory, and knowing already the parameters from joints 5, 6 and 7. The essential estimated parameters and their respective standard deviation are shown in Table 1, the position, velocity and acceleration of joint 4 are shown in Figure 7 and the validation of the estimated model is done in Figure 8.

The identified essential parameters are five: ZZR 4 and MYR 4 are regrouped inertial parameters, and FS 4 , FV 4 and τ off4 are three friction parameters corresponding to a simple model including Coulomb friction, viscous friction and a torque offset due to the asymmetrical Coulomb friction and other offsets introduced by measurement equipment, respectively. It can be seen that the torque reconstruction is excellent, being the percent error less than 0.5%. However, when analyzing the numerical value of the two parameters corresponding to the Coulomb friction, it can be noticed that it is theoretically impossible to have τ off4 > FS 4 , as it will lead to having the force of friction in the same direction as the velocity for a specific range. There are many alternatives to try to solve this issue. Two of them are: either the model does not explain the reality in a good way, for example, not being able to explain the Stribeck effect, thus another model has to be chosen, or constraints can be included in the optimization process of identification to ensure physical feasibility. Although the identification methods to be used with this dataset can be generalized to different robots, the identified parameters obtained using the information provided can be compared with previous works in [START_REF] Stürz | Parameter identification of the kuka lbr iiwa robot including constraints on physical feasibility[END_REF]; [START_REF] Hennersperger | Towards mri-based autonomous robotic us acquisitions: a first feasibility study[END_REF]; [START_REF] Xu | Dynamic identification of the kuka lbr iiwa robot with retrieval of physical parameters using global optimization[END_REF].

Human Interaction

In the context of pHRI, the safety of the person is the first and most important layer that has to be addressed. In order to accomplish that, the physical contact has to be recognized to react accordingly (either to detect collisions and react De [START_REF] De Luca | Collision detection and safe reaction with the dlr-iii lightweight manipulator arm[END_REF], or to collaborate based on the forces applied [START_REF] Mujica | Robust variable admittance control for human-robot co-manipulation of objects with unknown load[END_REF]). Recent manipulators, such as the KUKA iiwa, provide joint torque sensors that can be used for those purposes. Based on these sensors, torques on the joints can be used to detect and recognize collisions. Furthermore, in quasi-static condition, forces at different levels of the kinematic chain can be reconstructed through the virtual work principle. Therefore, the need of a Force/Torque sensor at the tip of the robot can be avoided, reducing the costs associated. This can be done by considering:

F e = J -T τ e , (1)
where F e is the external wrench (forces and torques) at the end effector level, τ e are the external joint torques, and J is the Jacobian matrix of the robot. Applying this method in the Sequence static 1 of the dataset, the forces applied at the end effector can be reconstructed as seen in Figure 9, using the external joint torque provided by the robot. However, in the figure, it can be noticed that the reconstructed force and the one of the F/T sensor (considered as the ground truth) present important differences. These differences can be linked to (1) where a quasi-static condition is considered and this may not be the case. Also, the presence of non-modeled dynamics in the model used by KUKA for the external torques can produce important differences (e.g., in the first 5 seconds, when no external forces or torques appear). Furthermore, in the proximity of a singularity, the inverse of the Jacobian is ill-defined, producing errors in this estimation. In recent years, improved methods to estimate forces at different levels of the kinematic chain have been considered [START_REF] De Luca | Collision detection and safe reaction with the dlr-iii lightweight manipulator arm[END_REF]. They presented advantages, like being able to estimate forces even without the need of the joint torques, but also some complexities like requiring a good model of the robot (e.g. non-modeled friction would easily degrade the results). For these reasons, this remains an open challenge. Different methods consisting of observers, filters or frequency analysis, can be used to identify, reconstruct and classify the interaction forces applied to the robot. In summary, this part of the dataset provides several sequences that allow testing and evaluating these methods on a real robot.

Conclusions and Future Work

This work presented the main features of the novel MESSII dataset, for the collaborative robot KUKA iiwa. The dataset contains an important number of sequences with different movements of the manipulator, with measurements of the propioceptive sensors and a F/T sensor attached to the end effector. This information allows the community to test and evaluate methods for identification of the robot, the sensor, and the load included, without the need to have the real robot or design and code the trajectories. Furthermore, as the dataset can be used in ROS to replay the sequences in real-time, online identification methods can be assessed. As the robot is used, in general, for human-robot interaction, the dataset also provides sequences where a person interacts with the robot. The goal is to allow the use of novel observers, filters and estimation to reconstruct the forces that appear at different levels of the kinematic chain, and compare them with the measurements of the Force/Torque sensor (ground truth). Beyond the structure and elements of the dataset, this paper presents examples of applications along with the main challenges that might motivate other researchers to use the MESSII dataset. In future works, this dataset will be enhanced with data from other robots as well as the use of different visual sensors to provide 3D information of the scene as well.

Figure 1 .

 1 Figure 1. IIWA robotic manipulator, payload and force-torque sensor.

Figure 2 .

 2 Figure 2. Industrial collaborative KUKA IIWA manipulator's structure.

Figure 3 .

 3 Figure 3. Framework of communication between the KUKA IIWA manipulator, the force-torque sensor and the external computer.

Figure 4 .

 4 Figure 4. Structure of the MESSII Dataset. The dataset is provided in a processed version to be used with ROS or not (Standalone version). Also, the raw data is provided.

Figure 5 .

 5 Figure 5. Sub-folders description of each of the possible applications of the MESSII dataset.

Figure 6 .

 6 Figure 6. Parameter identification procedure.

Figure 7 .

 7 Figure 7. Position, speed and acceleration of joint 4 in the trajectory Sequential Joint 4 Inertia Filtered.

Figure 8 .

 8 Figure 8. Comparison between actual and reconstructed torque of the trajectory Sequential Joint 4 Inertia Filtered with the identified parameters.

Figure 9 .

 9 Figure 9. Reconstructed forces using Sequence static 1 and the real ones obtained with the F/T sensor.

Table 1 .

 1 Identified essential inertial parameters and their respective relative standard deviation

	Param. Value	%σ
	ZZR 4 0.8600 0.06
	MYR 4 2.3283 0.05
	FS 4	0.0388 7.29
	FV 4	0.1154 2.63
	τ off4	0.4584 1.66

† http://www.robotous.com/ ‡ https://www.hp.com/


Jean-François Berret
email: jean-francois.berret@u-paris.fr

For applications of pulmonary surfactant delivery to the lungs, the question of rheology of the existing clinical formulations is of upmost importance. Recently, Ciutara and Zasadsinky (Soft Matter, 2021, 17, 5170-5182) measured the rheological properties of Infasurf®, Survanta® and Curosurf®, three of the most used pulmonary surfactant substitutes. This study revealed that these fluids are shear-thinning and characterized by a yield stress. The results obtained by Ciutara et al. on Curosurf® differ from our results published in Colloids and Surfaces B: Biointerfaces, 2019, 178, 337-345 and in ACS Nano, 2020, 14, 466 -475. In contrast, we found that Curosurf® suspensions are viscous Newtonian or slightly shear-thinning fluids, with no evidence of yield stress. The purpose of this Comment is to discuss possible causes for the discrepancy between the two studies, and to suggest that for biological fluids such as surfactant substitutes, the microrheology technique of rotational magnetic spectroscopy (MRS) can provide valuable results.

Introduction:

In the lungs, the alveoli form a froth-like structure and provide a large area that favors the transfer of the oxygen into the bloodstream and the carbon dioxide from the bloodstream into the exhaled air. 1,[START_REF] Notter | Lung Surfactant: Basic Science and Clinical Applications[END_REF] In mammals, the alveoli are constituted by an epithelium wall of thickness around 1 μm. One side of this epithelium is covered with lung lining fluid, also known as pulmonary surfactant and on the other side it is surrounded by blood capillaries. The pulmonary surfactant is made of phospholipids and proteins in a ratio 90:10 at the physiological concentration of 40 g L -1 . [START_REF] Hobi | [END_REF][4][5][6] The role of surfactant is to reduce the surface tension with the air and to prevent alveolar collapse and expansion during breathing 7,8 With regard to the inhalation of airborne nanoparticles, the pulmonary surfactant also represents an active protective barrier against external particles and pathogens. 9,10 In practice only few studies have investigated human or animal native (i.e. endogenous) pulmonary fluids, the reason being that they are difficult to extract, purify and condition to obtain significant reproducible data. [START_REF] Notter | Lung Surfactant: Basic Science and Clinical Applications[END_REF]8 Researchers have turned to pulmonary surfactant substitutes (i.e. exogenous), such as Infasurf®, Survanta® and Curosurf®, which are medications for treatment of preterm infants with acute respiratory distress syndrome (ARDS), a syndrome associated with the hyaline membrane disease. 11,12 The structural properties of exogenous surfactant are now well documented. Curosurf® for instance has been studied in details, and electron and optical microscopy have shown that the lipids associate into membranes to form multi-lamellar and multivesicular vesicles with size between 50 nm to 5 µm. [13][14][15] In contrast, their flow properties are much less known. However, these properties are critical in surfactant replacement strategies for children and adults 11,12,[START_REF] Lenclud | Curosurf® in Adult Acute Respiratory Distress Syndrome Due to COVID-19 (Caards-1)[END_REF] where fluid velocity in successive bifurcations can vary from 1 m s -1 in the trachea to 10 -3 m s -1 in the distal region of the lungs. [START_REF] Kazemi | [END_REF] Given the importance of the rheological properties of lung fluids for biomedical applications, it is surprising that only few rheology experiments have been performed yet. [18][19][20] Recently, Ciutara et al. measured the flow properties of Infasurf®, Survanta® and Curosurf® using cone-and-plate rheometry. 21 These authors were able to produce a consistent set of data showing that the three fluids were shear-thinning and characterized by a yield stress (𝜎 𝑌 ), implying that these fluids flow if a stress applied to the sample is greater than 𝜎 𝑌 . [22][23][24] In 𝜂(𝜎)flow curves, where 𝜂(𝜎) is the shear viscosity at the applied shear stress 𝜎, the existence of a threshold stress is seen by a sharp decrease in viscosity at 𝜎 = 𝜎 𝑦 (Figure 2 from Ref. 21 ). The yield stress values obtained were on the order of 𝜎 𝑦 = 0.02 Pa for Infasurf® and Curosurf®, and 𝜎 𝑦 = 1 Pa for Survanta®. The existence of residual elasticity at low frequencies has also been confirmed by the authors in linear rheology measurements, where the elastic and loss moduli 𝐺 ′ (𝜔) and 𝐺 ′′ (𝜔) show scaling laws as a function of the frequency with exponents around 0.4, together with the inequality 𝐺 ′ (𝜔) > 𝐺 ′′ (𝜔).

The results obtained by Ciutara et al. on Curosurf® differ from our results acquired by cone-andplate rheometry and by microrheology techniques. 25 The microrheology experiments were performed at Curosurf® concentrations between 5 and 80 g L -1 using remotely operated magnetic wires submitted to a rotating field. As described below, monitoring the wire behavior as a function of frequency provides access to the static shear viscosity and elastic modulus. These results were published in 2019 in the reference: 25 337-345 (2019). In this report, we find, in contrast to Ciutara et al. 21 that Curosurf® suspensions are viscous Newtonian or slightly shear-thinning fluids (depending on the concentration), with no evidence of a yield stress behavior. For applications of mimetic surfactant delivery, the question of rheology and in particular whether or not they are yield stress fluids is paramount. Such applications include surfactant replacement strategies applied to adults suffering from COVID-19 infection [START_REF] Lenclud | Curosurf® in Adult Acute Respiratory Distress Syndrome Due to COVID-19 (Caards-1)[END_REF][START_REF] Filoche | Proc. Natl. Acad. Sci[END_REF][START_REF] Grotberg | [END_REF] or less invasive surfactant administration (LISA) technologies for preterm infants. 28 In what follows, we first compare our macroscopic rheological data with those of Ciutara et al. 21 and recall the salient features of microrheology before concluding on the rheology of Curosurf®.

Comparison of rheological data from Ciutara et al. 21 and Thai et al. 25 : Fig. 1 compares the results obtained by the two groups in dynamical frequency sweeps for 𝐺 ′ (𝜔) and 𝐺 ′′ (𝜔) and at 40 and 80 g L -1 . All 𝜔-dependence can be accounted for by scaling laws of the form 𝐺 ′ (𝜔) ~ 𝜔 𝛼 and 𝐺 ′′ (𝜔) ~ 𝜔 𝛽 , as indicated by the straight lines fitting the data points. In Fig. 1, the exponents 𝛼 and 𝛽 equal 0.39 and 0.43 for the 80 g L -1 data from Ciutara et al., 21 and 𝛽 equals 0.95 and 0.75 from Thai et al. for 40 and 80 g L -1 , respectively. 25 Regarding 𝐺 ′′ (𝜔), the power law exponents and magnitudes differ, except at the highest frequency (~ 10 rad s -1 ) where they appear to intercept. The storage modulus 𝐺 ′ (𝜔) was also measured in the work of Thai et al. 25 In Supplementary Information S1, we show the strain (Fig. S1a) and frequency (Fig. S1b) sweep results obtained on Curosurf® 80 g L -1 . In Fig. S1b, 𝐺′(𝜔) is found to vary between 2×10 -3 and 2×10 -2 Pa in the range 0.1-10 rad s-1 and it is lower than 𝐺′′(𝜔). For G'(ω), data above 10 rad s-1 were removed from the plot, because in this range, G'(ω) was found to decrease with frequency. Because the 𝐺 ′ (𝜔)-data was not available across the entire frequency domain, it was decided not to include these data in the Thai et al. 2019 paper 25 or in the main text of this Comment. Taken together, both strain and frequency sweeps, in the ranges 0.5-100% and 0.1-10 rad s -1 show that Curosurf® 80 g L -1 is viscoelastic and characterized by a linear response dominated by the viscous part of the complex elastic modulus, i.e. 𝐺 ′′ (𝜔) > 𝐺 ′ (𝜔). 21 on Curosurf® suspensions at 40 and 80 g L -1 .The data in yellow are those of Fig. 5 in Ref. 21 An additional discrepancy between the two papers concerns steady shear data, where stress and viscosity are measured as a function of shear rate 𝛾̇. Figs. 2a and2c displays the stress versus shear rate 𝜎(𝛾̇) curves obtained for Curosurf® 80 g L -1 at 25 °C and 37 °respectively, whereas Figs. 2b and2d show the corresponding viscosity 𝜂(𝛾)-data. In Ciutara et al., 21 steady shear rheology was performed as a function of 𝛾̇ over the range 10 -2 -10 3 s -1 , the waiting time between each subsequent shear rate being 10 seconds. In Thai et al., 25 the stress versus shear rate curve was measured following first a ramp of velocity gradients starting from 10 -2 to 1000 s -1 (red dots), the entire scan lasting 15 minutes (measuring time 10 seconds and waiting time 20 seconds). At 1000 s -1 , the shear rate was decreased down to 10 -2 s -1 under similar waiting and measurement time conditions (blue dots). Following the approach suggested by Ovarlez and coworkers for complex fluids, 22,29 only the downward ramp data were considered in the Thai et al. paper, 25 as they allow overcoming the transient responses between two consecutive rates more easily than using an upward ramp. Moreover, in the published data (Fig. 2b in Ref. 25 ), only viscosity and stress values that were identical on the upward and downward ramps were retained, limiting the data to the 1 -1000 s -1 region. An interesting result here is that there is a reasonable overlap of the 𝜎(𝛾) ̇ and 𝜂(𝛾) ̇-data between the measurements by Thai et al. 25 and Ciutara et al., 21 typically above 5 s -1 . The differences between the upward and downward ramps suggest the existence of transient responses in the low shear rate domain, reminiscent of results found in the surfactant phases of wormlike micelles [START_REF] Lerouge | Polymer Characterization: Rheology, Laser Interferometry, Electrooptics[END_REF] and bilayers. [START_REF] Berni | [END_REF][32][33] Note that although Curosurf® membrane has the gel-to-fluid transition temperature at 29.5 °C (Supplementary Information S2), the Curosurf® viscosities at 25 and 37°C exhibit similar shear-thinning behaviors above 1 s -1 , indicating a weak temperature dependence (Supplementary Information S3). In conclusion of this part, we cannot exclude that the differences between the measurements in the two groups are due to the different protocols used. The results of both studies are close to each other for 𝐺 ′′ (𝜔) at high angular frequency and for the shear stress at high shear rates, but differ in the low frequency and shear rate regions. 25 following a ramp of velocity gradients from 10 -2 to 1000 s -1 (resp. from 1000 s -1 to 10 -2 s -1 ), whereas the data in yellow are from Ciutara et al. 21

Magnetic wire active microrheology data on Curosurf® as a function of the lipid concentration

Recently, we applied the magnetic rotational spectroscopy (MRS) technique to determine the viscoelastic properties of complex fluids such as surfactant wormlike micelles, 34 polysaccharide gels, 35 the cytoplasm of living cells, 36 DNA strands complexed with amyloid fibers 37 and pulmonary mucus. 38 As mentioned above, it has also been applied to Curosurf® samples as a function of the concentration and in the presence of engineered nanoparticles, as shown in Thai et al, ACS Nano 14, 466 -475 (2020). 39 With MRS, magnetic wires of length between 1 and 100 µm, and of diameters 200 nm to 2 µm are submitted to a rotational magnetic field at increasing angular frequency 𝜔 and the wire motion is monitored by time-lapse microscopy. In its current configuration, the MRS allows to measure viscosity between 10 -3 and 10 3 Pa s and elasticity from 0.1 to 100 Pa over a frequency range between 10 -3 and 100 rad s -1 . The generic model of magnetic wire embedded in a viscous Newton liquid of static shear viscosity (Fig. 3a) 𝜂 predicts that at low frequency the wire rotates in phase with the field, leading to a synchronous motion. 40 With increasing 𝜔, the friction torque increases and above the critical value 𝜔 𝐶 the wire undergoes a transition towards an asynchronous regime at: 40

𝜔 𝐶 = 3 8𝜇 0 Δ𝜒 𝜂 𝐵 2 𝐿 * 2 (1)
In Eq. 1, 𝜇 0 is the vacuum permeability, Δ𝜒 the anisotropy of susceptibility between parallel and perpendicular wire direction, 𝐵 the magnetic field and 𝐿 * = 𝐿 𝐷√𝑔(𝐿 𝐷 ⁄ ) ⁄

, with 𝑔(𝑥) = 𝑙𝑛(𝑥) -0.662 + 0.917/𝑥 -0.050/𝑥 2 . 34 With MRS, the simplest method to retrieve 𝜂 is to measure the critical frequency 𝜔 𝐶 as a function of the reduced wire length 𝐿 * and to verify the 1/𝐿 * 2dependence. The static viscosity is then determined from the prefactor 3Δ𝜒𝐵 2 /8𝜇 0 𝜂. We further developed the concept of rotating wires applying it in soft solids such as crosslinked polysaccharide gels. 35 For soft solids, the critical frequency 𝜔 𝐶 is identically zero whatever the frequency, and the wires oscillates between two symmetric orientations of amplitudes 𝜃 𝐵 (𝜔). This behavior can be understood with the help of Eq. 1 by assuming an infinite value for the viscosity, or equivalently by the fact that the stress applied is lower than that of the yield stress, the material being solely subjected to a deformation. In the asymptotic low and high frequency regimes, one gets for soft solids: 35 where 𝜃 𝑒𝑞 = 3Δ𝜒𝐵 2 /4𝜇 0 𝐺 𝑒𝑞 𝐿 * 2 and 𝜃 0 = 3Δ𝜒𝐵 2 /4𝜇 0 𝐺𝐿 * 2 (2𝑏)

where 𝐺 𝑒𝑞 and 𝐺 denote the equilibrium and static storage elastic moduli, respectively. Table 1 summarizes the generic behaviors of a magnetic wire subjected to a rotating field as a function of frequency when placed in one of the four basic models of rheology, i.e. those of Newton, Maxwell, the Standard Linear Solid and Hooke. 41,[START_REF] Larson | The Structure and Rheology of Complex Fluids[END_REF] The signatures of each model are clearly established, and show that the MRS method can differentiate between a viscous fluid and a soft solid. This can be achieved by studying the occurrence of the synchronous/asynchronous transition (column 4, Table 1) or the oscillation amplitude as a function of frequency (column 5, Table 1). We will use the predictions in Table 1 to identify the rheological nature of the Curosurf® (Fig. 3b).

Fig. 3c displays the ratio 8𝜇 0 𝜂𝜔 𝐶 /3Δ𝜒𝐵 2 as a function of the reduced wire length 𝐿 * for Curosurf® samples at concentration 5, 20, 40, 50, 70 and 80 g L -1 . The data points are found to collapse on a single master curve displaying the 1/𝐿 * 2 -dependence (straight line). This set of results shows that according to Table I, all the samples studied obey a Newton or Maxwell type behavior. The data on the oscillation amplitude in Ref. 25 confirm that at physiological concentration 𝜃 𝐵 (𝜔)~𝜔 -1 and that lim 𝜔→∞ 𝜃 𝐵 (𝜔) = 0, suggesting finally a Newton-like behavior.

At the concentration of the clinical formulation (80 g L -1 ), 𝜃 𝐵 (𝜔) was found to deviate slightly from the Newton prediction, an outcome that was interpreted as the onset of viscoelasticity and could also be linked to the shear-thinning behavior in steady shear. 41,[START_REF] Larson | The Structure and Rheology of Complex Fluids[END_REF] The synchronous-asynchronous transition observed ion Curosurf® 40 g L -1 can be viewed in the Supporting Information movies in Refs. 25,39 . The values of the static viscosity used to construct the master diagram in Fig. 3c are displayed in Fig. 3d as a function of the Curosurf® concentration. At low concentration, 𝜂(𝑐) is increases linearly (dotted line) and deviates from the linear behavior above 40 g L -1 . The continuous line through the data points was obtained using a modified Krieger-Dougherty equation, [START_REF] Krieger | [END_REF] 𝜂(𝑐) = 𝜂 𝑆 (1 -𝑐/𝑐 𝑚 ) -2 where 𝜂 𝑆 is the solvent viscosity, 𝑐 𝑚 the concentration at which the viscosity diverges and where the exponent in the function (1 -𝑐/𝑐 𝑚 ) was set to -2. 44 For Curosurf®, we found 𝑐 𝑚 = 117 g L -1 . Assuming that 𝑐 𝑚 is related to the maximum-packing volume fraction 𝜙 𝑚 of vesicles and that its value for dispersed colloids is 0.63, 45,46 we end up with a volume fraction for the Curosurf® formulated at 80 g L -1 of 𝜙 = 0.42, in good agreement with recent literature determinations. 20,21 Fitting the viscosity data using the Krieger-Dougherty three-parameter model [START_REF] Krieger | [END_REF] yields a similar continuous line in Fig. 3d, with 𝑐 𝑚 = 101 g L -1 and an exponent equal to 1.54. As a conclusion to this section, we have found that the results of microrheology on Curosurf®, whether as a function of frequency or concentration, are consistent with a description in terms of colloidal suspensions that is below the critical volume fraction 𝜙 𝑚 . In contrast to the paper by Ciutara et al., 21 all studied suspensions were of Newton type (or slightly viscoelastic)) and no yield stress behavior could be evidenced.

Rheological model

Static shear viscosity

In the course of this work, we questioned the ability of the MRS technique to detect low yield stresses (< 1 Pa), such as those reported by Ciutara et al. 21 for mimetic surfactants. In practice, we cannot exclude cases where the wires driven by the rotating magnetic field would disrupt the vesicle network, and locally induce flow. To answer this question, we return to the recent study we did on the effects of engineered nanoparticles on Curosurf® rheology. In this work, we studied the effects of 40 nm cationic silica (SiO2) and alumina (Al2O3) nanoparticles on Curosurf® properties formulated in physiological conditions. It was found that particles interact strongly with Curosurf® vesicles, inducing profound modifications in the surfactant flow properties. In particular, we could show that above the alumina concentration of 0.1 g L -1 , Curosurf® underwent a rheological transition, from a purely viscous liquid to a soft solid behavior (described by the Standard Linear Model in Table 1). The transition was interpreted in terms of a bond percolation network, the particles acting as cross-links to the vesicles. Interestingly, the equilibrium elastic modulus 𝐺 𝑒𝑞 in Al 2 O 3 -Curosurf® mixtures (Eq. 2) was found in the range 0.01 -0.1 Pa, and increasing with the particle concentration. For Curosurf® at 80 g L -1 , Ciutara et al. found low frequency storage modulus of the order of 0.1 Pa (Fig. 1), suggesting that if the Curosurf® formulation studied in Refs. 25,39 had been a soft solid with a finite yield stress, the MRS technique should have be able to detect it, which was not the case. These latter results represent a further indication of the differences in rheological response of Curosurf® studied by Thai. et al. 25 and by Ciutara et al. 21 .

Conclusion:

We have shown in this Comment that from the macroscopic rheology and active microrheology data operating on the MRS principle, the Curosurf® samples showed, at all concentrations studied, a Newtonian or slightly viscoelastic behavior, in contradiction with the results from Ciutara et al. 21 who proposed that pulmonary surfactants are yield stress fluids. The concentrated Curosurf® suspension shows flow curves that suggest transient responses at low shear rates, as illustrated by the differences between the up-and downward ramps in Fig. 2. It should be recalled that many complex self-assembled fluids, including surfactant lamellar phases show transient behavior at low velocity gradients that can last for from minutes to hours. [START_REF] Berni | [END_REF][32][33] Step shear rate experiments over extended periods of time are well suited to monitor these transient responses. They are however difficult to perform on Curosurf® because of the large amount of sample required. Here we show that difficulties inherent to classical rheometry, and in particular with regard to yield stress identification, [22][23][24] can be solved using our wire-based microrheology technique.

Figure 1 :

 1 Figure 1 : Compilation of data of 𝐺 ′ (𝜔) and 𝐺 ′′ (𝜔) measured by Thai et al. (T = 25 °C)25 and by Ciutara et al. (T = 37 °C)21 on Curosurf® suspensions at 40 and 80 g L -1 .The data in yellow are those of Fig.5in Ref.21

Figure 2 :

 2 Figure 2 : a, b) Shear stress and viscosity versus shear rate curves for Curosurf® 80 g L -1 at T = 25 °C. c,d) Same as in a) and b) for T = 37 °C. The data in red (resp. blue) are from Thai et al.25 following a ramp of velocity gradients from 10 -2 to 1000 s -1 (resp. from 1000 s -1 to 10 -2 s -1 ), whereas the data in yellow are from Ciutara et al.21

Figure 3 :

 3 Figure 3: a) Schematic representation of a wire actuated in a Newton viscous liquid represented by a dashpot. In MRS, the magnetic field rotates at a constant angular frequency 𝜔. b) Phasecontrast optical microscopy image of a 40 g L -1 Curosurf® dispersion at 25 °C (objective 20×) showing a 64 µm long magnetic wire. Arrows are pointing to vesicles. c) Normalized critical frequency 8𝜇 0 𝜂𝜔 𝐶 /3𝛥𝜒𝐵 2 as a function of the reduced wire length 𝐿 * obtained for Curosurf® suspensions at concentration 0 to 80 g L -1 (𝑇 = 25 °C).25 The straight line displays the 1/𝐿 * 2dependence predicted for Newton fluids (Eq.1). d) Concentration dependence of the Curosurf® static viscosity. The dotted line is from the Einstein model while the continuous line is derived from a modified Krieger-Dougherty equation.44

Table 1 :

 1 Summary of the predictions for the wire rotation in viscous (Newton) and viscoelastic (Maxwell) liquids, and in viscoelastic (Standard Linear Solid) and elastic (Hooke) solids.

			Yield stress	Sync./Async. transition	𝝎 𝑪	𝐥𝐢𝐦
	Newton	𝜂	No	Yes	Eq. 1	0
	Maxwell	𝜂 = 𝐺𝜏	No	Yes	Eq.1	𝜃 0
	Standard Linear Solid	infinite	Yes	No	0	𝜃 0 𝜃 𝑒𝑞 /(𝜃 0 + 𝜃 𝑒𝑞 )
	Hooke	infinite	Yes	No	0	𝜃 𝑒𝑞

𝝎→∞ 𝜽 𝑩 (𝝎)

Acknowledgments

We thank Mostafa Mokhtari and his team from the neonatal service at Hospital Kremlin-Bicêtre, Val-de-Marne, France for providing us the Curosurf® suspensions and Sandra Lerouge, Jesus Perez-Gil and Christophe Lenclud for fruitful discussions. Imane Boucema is acknowledged for letting us use the Anton Paar rheometer for the cone-and-plate rheology. This research was supported in part by the Agence Nationale de la Recherche under the contract ANR-12-CHEX-0011 (PULMONANO) and ANR-17-CE09-0017 (AlveolusMimics).


2/19

Introduction Algorithm for noise generation Results Discussion & conclusions (Supplementary)

Phoneme discrimination using the ACI method Phoneme discrimination using the ACI method: Optimisation? Phoneme discrimination using the ACI method: Optimisation?

• Other speech samples Rationale: speeding up the ACI assessment

Rationale: Hypotheses

Using bump noises:

• H1: We will be able to obtain clean ACIs: pilots with one participant

• H2: Different sets of noises will lead to the same ACIs: to be checked by the model Experimental design:

H1 -Experiments

• H1: Yes, we were able to obtain clean ACIs, but... H2 -ACIs from simulations

• H2: Yes, the ACIs were independent from the set of bump noises Comparing ACIs from experiments/simulations (1 of 2) Int. representations at fc=1250 Hz

•

  N trials needed • N is too high (> 4000) 4/19 Introduction Algorithm for noise generation Results Discussion & conclusions (Supplementary)

•

  Fig. 1

•

  Baseline: White noises • Data collection from 12 participants (4000 trials ≈ 4h sessions x noise type x participant) noise generation Results Discussion & conclusions (Supplementary)

  Fig. 3

  Fig. 4

11Fig

  Fig. 4a

Using the auditory model: possibilities and limitations

• Individualisation of the model?

• This model was developed to simulate psychoacoustic tasks • Hearing impairment can be introduced, but it is not straightforward:

We cannot introduce an audiogram as in other models (e.g., from AMT [START_REF] Majdak | AMT 1.x: A toolbox for reproducible research in auditory modeling[END_REF]]: zilany2014, bruce2018) 2 Impairment can be introduced by this requires a careful understanding of the model stages and their expected effect [START_REF] Holube | Speech intelligibility prediction in hearing-impaired listeners based on a psychoacoustically motivated perception model[END_REF])

Conclusions

ACI method

• Assessment of individual listening strategies

• Interesting tool to obtain T-F cues for both models and participants Use of auditory models (my main focus today)

• "Optimal integration of cues" • Can be used to support/reject hypotheses • Careful: T-F cues may not reflect the actual (but candidate) cues

• Careful: There might be results that are model dependent I still believe that much can be learned from auditory models and the estimated internal representations

Thank you for your attention

• Questions or comments? Osses & Varnet (2022). fastACI toolbox: the MATLAB toolbox for investigating auditory perception using reverse correlation (v1.2). doi:10.5281/zenodo.7314014. GitHub: github.com/aosses-tue/fastACI


Yves André

Grothendieck and differential equations

Introduction

There is an important, original and varied part of Grothendieck's work devoted to differential equations, a part which had a long posterity and which we would like to delineate.

Scattered in several texts and less documented, it is not so well-known as other parts of his work. To begin with, the expression "differential equation" does not even seem to appear under his pen... This paradoxical fact deserves a moment's thought. Dealing with mysteries and differential equations, a starting point soon comes to mind, namely: 6accdae13eff7i3l9n4o4qrr4s8t12ux. This is Newton's answer (1677 1 ) to Leibniz' query about his methods of invention: begging the question or rather hiding the answer in a mysterious sentence containing six times the letter a, twice the letter c, one d, one diphthong ae, etc. Scholars deciphered the anagram as follows:

Data aequatione quotcunque fluentes quantitates involvente, fluxiones invenire; et vice versa -note that there are 9 t's, not 8: Newton's or the decipherers' mistake? Anyway, this is often grossly translated from latin to english as it is useful to solve differential equations.

The immense development of the theory of differential equations and its applications after Newton gives fully right to this saying, namely to the importance of solving differential equations or studying their solutions.

Nevertheless, some three centuries later, Grothendieck took an opposite view, which could be phrased as follows:

it is also useful not to solve differential equations, but to study their structure.

Solutions versus structure: this fundamental tension is reminiscent of its counterpart in algebraic geometry, and of the way Grothendieck overcame it, thanks to the functorial viewpoint: generalizing the notion of point (a solution of algebraic equations) and viewing a variety as the object which represents the functor of its (generalized) points.

But Grothendieck never developed a similar viewpoint for differential equations instead of algebraic equations 2 .

1 "The foundations of these operations is evident enough, in fact; but because I cannot proceed with the explanation of it now, I have preferred to conceal it thus: 6acc-dae13eff7i3l9n4o4qrr4s8t12ux. On this foundation I have also tried to simplify the theories which concern the squaring of curves, and I have arrived at certain general Theorems".

2 A differential-algebraic geometry has since been developed in various guises, but it is not based on the functorial viewpoint.

Differential operators.

In the context of a linear differential equation L y = 0, the two viewpoints in tension are summarized by the emphasis on the study of the differential operator L, or of the solutions y.

It is more or less equivalent to consider a linear differential system

∂ y = A y,
where A is a matrix, and this leads to the more intrinsic notion of differential modules or integrable connections: namely, a map T S ∇ → End k M satisfying Leibniz's rule and commuting with the Lie bracket. Such an action of T S extends to its "enveloping algebra" D S , which endows M with a structure of D S -module.

Grothendieck's contribution [START_REF] Grothendieck | Eléments de géométrie algébrique[END_REF] stems from his recasting differential calculus in terms of infinitesimal neighborhoods of the diagonal in S 2 . By duality, he defines a ring of differential operators Dif f S = ∪Dif f ≤n S , and gives a very simple inductive characterization: L ∈ Dif f n S if and only if L ∈ End k O S and for any section

f of O S , [L, f ] ∈ Dif f n-1 S
. In particular, he recovers in this way the tangent bundle and Ehresmann's jets3 , cf. [START_REF] André | De Rham cohomology of differential modules on algebraic varieties[END_REF]II].

One has a map D S → Dif f S which is an isomorphism in characteristic 0, but which is neither injective nor surjective in characteristic p > 0.

In char. p and in one variable, Dif f S corresponds to Schmidt's iterated divided derivations -whence two languages, and a further one: infinitely Frobenius-divisible modules. The lively (albeit a little exotic) theory of Dif f S -modules (Gieseker, Esnault...) makes full use of triple viewpoint.

Grothendieck and his school (Berthelot...) showed that the "good version" of D S in char. p, which restores the link with integrable connections, consists in endowing the ideals of infinitesimal neighborhoods of the diagonal with divided powers [START_REF] Berthelot | Notes on crystalline cohomology[END_REF].

In the meantime, inspired by the theory of formal groups and de Rham cohomology (see below), he initiated his crystalline theory [START_REF] Grothendieck | Crystals and the de Rham cohomology of schemes[END_REF], first announced in his famous letter to Tate (1966): un cristal possède deux propriétés caractéristiques: la rigidité, et la faculté de croître dans un voisinage approprié.

In a first version, those appropriate neighborhoods were locally nilpotent closed immersions of open subsets of the base S. In this setting, a crystal in modules amounts to a quasi-coherent module M over S together with an isomorphism χ : p * 1 M ∼ = p * 2 M (where p 1 , p 2 are the projections of the formal completion of the diagonal of S 2 to S), satisfying a cocyle condition; and this corresponds exactly to a Dif f S -module.

Let us emphasize that the novelty does not lie in the construction (indeed, the isomorphism χ is nothing but the classical resolvant of the corresponding differential system), but in the interpretation: here, χ is seen as a descent data in the infinitesimal site.

In a later version, Grothendieck introduced divided powers in the definition of crystals, initiating a theory which was largely developed by Berthelot and others [START_REF] Berthelot | Notes on crystalline cohomology[END_REF]. Beyond technical aspects, let us note here the novelty which consists in seeing certain p-adic differential systems as attached to a variety in char. p rather than to a p-adic variety, which allows a functorial explanation of the action of Frobenius on such systems (discovered "experimentally" by Dwork).

Coming back to char. 0, let us recall that the theory of D-modules was mainly developed later under the name "algebraic analysis" in the wake of other traditions: (Sato and) Kashiwara [START_REF] Kashiwara | Algebraic study of systems of partial differential equations[END_REF], or Bernstein, to quote the founders. It relies on key concepts like the characteristic variety and holonomy, and on a powerful homological viewpoint which integrates the solution viewpoint and goes beyond, putting solutions and cosolutions4 on equal footing.

One could say that in char. 0, integrable connections and D-modules are equivalent in theory but not in practice -the two viewpoints being rather different: the theory of connections restricts itself to the case of O S -coherent modules, which amounts to rejecting singularities to infinity, whereas the theory of D-modules does not and includes Dirac distributions for instance in its setting.

Singularities.

The saying "you never understand a domain so well as through its crises" is especially relevant in the context of differential equations. The study of the behaviour of the solutions of a linear differential equation Ly = 0 with meromorphic coefficients, in the neighborhood of a singularity5 is a rich and subtle theme which takes its roots in the classical works of Fuchs and Poincaré. This will lead us through a long historical detour, at the end of which Grothendieck's viewpoint will reappear.

One has two different ways for zooming at the singularity: 1) one can localize L at a disk D where there is only one singularity (its center), and then pass to the formal completion (i.e. consider the coefficients of L as formal power series).

The problem becomes purely algebraic; it turns out that after finite ramification, L factors as a product of differential operators of order 1 (Levelt).

2) One can restrict L to the punctured disk D * (i.e. consider the coefficients of L as analytic functions in D * ).

The problem becomes purely topological, and is controlled by the local monodromy.

The favorable situation is the case of a regular singularity (Fuchs 1866, Frobenius 1873, cf. [START_REF] Gray | Linear differential equations and group theory from Riemann to Poincaré[END_REF]). In this case, the algebraic theory 1) and the topological theory 2) match: the formal decomposition of L is meromorphic. The condition of regularity is expressed by a simple inequality involving the valuations of the coefficients of L.

But in the case of an irregular singularity, some divergent series appear in the algebraic factorization, and the bridge between the algebraic theory and the topological theory becomes much more indirect, going through the theory of asymptotic expansions by zooming to the singularity along sectors, cf. [10][21]. This short account does not follow, admittedly, the incredibly tortuous historical path: in fact, the key point in the irregular case -the so-called Stokes phenomenon (1847-58) -predates by two decades the definition of a regular singularity (1866-73).

The theory of differential equations with regular singularities has enjoyed great fortune, due to the fact that the local correspondence with monodromy extends to the global situation. This is the so-called Riemann-Hilbert correspondence. "Equations différentielles à points singuliers réguliers" is the title of a famous memoir where Deligne establishes this correspondence between regular integrable connections and local systems on a smooth complex algebraic variety.

The theory got a second wind thanks to the homological viewpoint of the theory of D-modules, where the Riemann-Hilbert correspondence finds its natural extension in the derived setting. Very recently, the theory has been extended to the irregular case, cf. [START_REF] Guillermou | Le problème de Riemann-Hilbert dans le cas irrégulier (d'après D'Agnolo[END_REF].

Remark. One finds several different definitions of regularity in the literature, and their equivalence cannot be taken for granted, especially in several variables. Deligne [START_REF] Deligne | Equations différentielles à points singuliers réguliers[END_REF] shows an equivalence between an analytic definition (moderate growth of solutions in the neighborhood of a singularity) and various algebraic definitions, notably one by restriction to curves. However, the argument is incorrect -it overlooks the phenomenon of confluence -and Deligne replaced it by a transcendental argument. The question of providing an algebraic proof of the equivalence of the algebraic definitions remained open for some time, until I solved it using the theory of irregularity [START_REF] André | De Rham cohomology of differential modules on algebraic varieties[END_REF]VI].

For Kashiwara, regularity corresponds to reduceness of the characteristic variety; the fact that this matches with Deligne's conditions is not at all obvious and was proved only recently [START_REF] Cailotto | Algebraic connections vs. algebraic D-modules: regularity conditions[END_REF].

Let us now turn to the p-adic case: it is in this situation that Grothendieck's crystalline viewpoint played a decisive role, in the way of conceiving what a singularity really is.

The solutions y of a p-adic differential equation Ly = 0 usually do not converge up to the next singularity (for instnce y = e t , solution of dy dt -y = 0, has radius of convergence p -1/(p-1) ). Dwork, the founder of the theory, stressed the importance of radii of convergence of solutions, and introduced the notion of overconvergence and of Frobenius structure, which allowed him to select a good category of differential equations (which turned out to correspond to overconvergent F -isocrystals in Berthelot's setting). Following Grothendieck's viewpoint, one should consider overconvergent p-adic differential equations as "living" in char. p, which leads to consider singularities no longer as points, but as open discs. Overconvergence allows to enter a little into those singular discs. The analog of studying a complex-analytic L by restriction to the punctured disc (with center the singularity) becomes, in the p-adic case, restricting to a thin annulus at the inner boundary of the singular disc.

This viewpoint, advocated by Crew, progressively led to an essentially complete understanding of p-adic differential equations in the framework of Berkovich geometry (Christol-Mebkhout, Baldassarri, Kedlaya, Pulita-Poineau... cf. [20][8]).

Gauss-Manin connection.

This is Grothendieck's central contribution to differential equations.

In his letter to Atiyah (1963, augmented and published as [START_REF] Grothendieck | On the de Rham cohomology of algebraic varieties[END_REF]), Grothendieck defines algebraic De Rham cohomology of a smooth algebraic variety in char. 0 (hypercohomology of the algebraic De Rham complex), and shows that this provides a reasonable theory: it gives the usual Betti numbers. This short but incredibly rich letter goes beyond. For instance, Grothendieck observes that the comparison isomorphism between the transcendental Betti cohomology and his algebraic De Rham cohomology gives rises to some classical constants (the periods), which were studied in transcendental number theory; in a cryptic footnote, he alludes to a general transcendence conjecture about them without stating it (the now famous Grothendieck period conjecture).

In the relative case, i.e. when the periods depends on a parameter, it had been known since the XIX century that they are solutions of a linear differential equation with algebraic coefficients: the Picard-Fuchs equation, cf. [START_REF] Gray | Linear differential equations and group theory from Riemann to Poincaré[END_REF].

The prototype is Gauss hypergeometric equation ( 1812)

t(1 -t) d 2 y dt 2 + (c -(a + b + 1)t) dy dt -ab y = 0 satisfied by ∞ 1 z a-c (1 -z) c-b-1 (1 -tz) -a dz.
The problem posed by Grothendieck is to give an algebraic construction of the connection of which the periods are solutions. In the case of a family of curves (Fuchs 1871), Manin had just provided such an algebraic connection.

The problem to construct an algebraic connection on algebraic relative de Rham cohomology amounts to understanding algebraically "integration in the fiber". This problem seems so fundamental in Grothendieck's view that he does not hesitate to change the established terminology and replace "Picard-Fuchs" by "Gauss-Manin" in order to underline the change of viewpoint, bracketing a century work on Picard-Fuchs equations without having yet any result to propose! Soon after, however, he had such a construction. Katz and Oda proposed a more general one, with coefficients in an arbitrary integrable connection, cf. [START_REF] André | De Rham cohomology of differential modules on algebraic varieties[END_REF]VII]. This was the beginning of the yoga of De Rham coefficients, in Grothendieck's terms, which reached maturity with the formalism of the six operations in Kashiwara's theory of holonomic D-modules.

In the p-adic case, Berthelot came to a synthesis between the crystalline and the D-module viewpoints: the theory of D † -modules [START_REF] Berthelot | Introduction à la théorie arithmétique des D-modules[END_REF]. However, the yoga of p-adic De Rham coefficients started to work only after combination with the transcendental study of p-adic singularities (Caro).

Remark. By the way, is Grothendieck-Katz-Oda's Gauss-Manin connection the same thing as the direct image in the sense of D-module theory?

During the last quarter of the XXc., the question has been relegated in the folklore, the answer often taken for granted and not worth being written down... until Dimca, Maaref, Sabbah, Saito (2000) took the pain to write down two proofs [START_REF] Dimca | Dwork cohomology and algebraic D-modules[END_REF]; the simplified proof given in [START_REF] Cailotto | Algebraic connections vs. algebraic D-modules: regularity conditions[END_REF] is still far from being simple.

A further remark. Let us come back to the starting point: Gauss hypergeometric equation with parameter a = 1/2, b = 1/2, c = 1, which controls the variation of periods of the Legendre family of elliptic curves. In many courses and articles, one can read the monodromy matrices 1 2 0 1 at 0, 1 0 -2 1 at 1, often followed by the "well-known" fact that they generate the subgroup Γ(2) of GL2(Z) consisting of matrices congruent to id mod.2: "well-known", but wrong! 6

5. Galois aspects.

Algebraic functions satisfy linear differential equations. The idea to generalize generalize Galois theory from algebraic equations to differential equations (maybe foreseen by Galois, and initiated by Liouville) took shape when Picard (1883) defined the differential Galois group attached to a linear differential equation Ly = 0: form the extension of the field of coefficients generated by the solutions y and their derivatives; the differential Galois group is the automorphism group of this extension of differential fields. This is an algebraic group which acts linearly on the spaces of solutions.

Galois theory became increasingly efficient with the development of finite group theory (in practice, the Galois correspondence is applied in one direction); similarly, differential Galois theory became useful with the development of linear algebraic group theory, and was one of its main early motivations (Kolchin), cf. [START_REF] Van Der Put | Galois theory of linear differential equations[END_REF].

Apparently, Grothendieck has never shown any interest for this theory. This is strange if one considers Grothendieck's creation of the theory of the etale fundamental group, and even more if one considers his theory of tannakian categories, which are linear analogues of discrete Galois categories -in fact, Deligne developed a tannakian interpretation of differential Galois theory.

One reason could be that (until recently) differential Galois theory was a theory of differential fields only: it turns out that in order to get a Galois theory of differential algebras and schemes, one needs more than the classical tools (groups and torsors), namely the theory of quasi-homogeneous varieties [START_REF] André | Algèbres de solutions d'équations différentielles et variétés quasi-homogènes: une nouvelle correspondance de Galois différentielle[END_REF].

Another reason could be that Grothendieck did not know that on replacing monodromy groups by monodromy groupoids, one gets rid of the regularity condition: the Zariski closure of the monodromy groupoid is always the differential Galois groupoid (Cartier, Malgrange cf. [7, §5]) 7 .

There are nonetheless two contact points between Grothendieck's theory of the etale fundamental group and differential Galois theory.

1) the situation where the two theories are trivial: if S is proper smooth and if π et 1 (S) = 0, then there is no non-trivial D-module on S (Grothendieck).

2) Grothendieck's p-curvature conjecture (a differential analogue of the fact that Galois groups of number fields are generated by Frobenii). This stems from Fuchs's influential question (1875): characterize those differential equations which have a full set of algebraic solutions 8 .

Grothendieck's conjecture predicts that this happens when this happens modulo p for almost all p (which translates into the vanishing of p-curvatures). Its analog is known in equal char. 0 (Hrushovsky, myself) and in equal char. p (Esnault-Mehta), but still open in mixed characteristic, i.e. in the original setting.

6 Γ(2) is the product of the monodromy group by {±1}. 7 for instance for y = e t , the monodromy group is trivial while the differential Galois group is C * ; but the monodromy groupoid is given by the graph of (t 1 , t 2 ) → e t 2 -t 1 which is Zariski-dense in the differential Galois groupoid C × C × C * .

8 this question lies at the source of the uniformization theorem of algebraic curves (Poincaré-Koebe), cf. [START_REF] Gray | Linear differential equations and group theory from Riemann to Poincaré[END_REF].

Conclusion

In this text, I put forward viewpoints rather than results, since many of Grothendieck's contributions to the theme "differential equations" lie in his novel viewpoints: differential operators, infinitesimal and crystalline topoi, algebraic de Rham cohomology and the Gauss-Manin connection... Even restricted to the domain of algebraic analysis considered in this article, there is a remarkable plurality -sometimes a plethora -of viewpoints on differential equations. The subject often gets advantage of the crossed perspectives; but occasionally, they ignore each other for lack of dictionaries between different languages. Such dictionaries are as rare as valuable: the variations which they allow help keeping fertile a viewpoint -those fertile viewpoints about which Grothendieck once wrote [START_REF] Grothendieck | Récoltes et Semailles[END_REF]:

Le point de vue fécond est celui qui nous révèle, comme autant de parties vivantes d'un même Tout qui les englobe et leur donne un sens, ces questions brûlantes que nul ne sentait, et (comme en réponse peut-être à ces questions) ces notions tellement naturelles que personne n'avait songé à dégager, et ces énoncés enfin qui semblent couler de source, et que personne ne risquait de poser, aussi longtemps que les questions qui les ont suscités, et les notions qui permettent de les formuler, n'étaient pas apparues encore. Plus encore que ce qu'on appelle les théorèmes-clef en mathématique, ce sont les points de vue féconds qui sont, dans notre art, les plus puissants outils de découverte -ou plutôt, ce ne sont pas des outils, mais ce sont les yeux même du chercheur qui, passionnément, veut connaître la nature des choses mathématiques.

this viewpoint as well as Grothendieck's infinitesimal topos were rediscovered later, in the guise of the so-called "synthetic geometry".

i.e. elements of the cokernel of the differential operator.

i.e. a pole of the coefficients.


Window 3 Earliest Cultures and their Time Frames along the Coastlands of Oman

Vincent Charpentier

The identification of the hunter-gatherer societies of the beginning of the Early Holocene, is an important theme for research in Oman Peninsula. The chronology of the techno-cultural facies of Fasad, long based on conjecture, which we know today to belong to the first half of the 8 th millennium BC, a period of high precipitation that should be correlated with the intensification of the south-west monsoon. The elements characteristic of this assemblage are projectile points made on blanks of flakes that are thin or sometimes thick; blade products are rarer. The tang is generally fashioned by bifacial retouch, sometimes simply direct or inverse, rarely alternately. The distal extremity of these points is naturally sharp and not retouched, although some are sometimes reworked by a series of short marginal retouching. Absent from Yemen, except for the Hadramaut and the Mahra where its presence is slight, this cultural entity is well represented in some localities of Dhofar, the only region having produced stratified sites (Jebel Qara, Nedj, etc.). In Oman Peninsula, Ras Al-Jinz 37, is actually the unique stone dwelling known for this period. Since the early Holocene, most of the occupations of this period have suffered the effects of strong winds or violent erosion and the remains in place are rare.

The role of autochthonous cultures in the appearance of the first producer societies, and the influence of the PPNB of the Levant in the emergence of the Neolithic in the Oman peninsula are themes that remain crucial for research.

Between 6500 and 3100 BC, fully "Neolithised" cultures developed in the peninsula. Except for the Gulf, the earliest culture from Oman to Yemen was characterised by the domestication of Caprinae and the presence of pressure-retouched trihedral points sometimes "fluted". In the Ja'alan, this period was the object of excavation at Suwayh SWY-1, of which the stratigraphy covering the period 5700-4200 BC is exceptional.

Vincent Charpentier • Inrap, UMR 7041 • vincent.charpentier@inrap.fr The earliest habitation structures are set directly upon the beach-rock. a circular structure of about 2 m in diameter with a long ditch associated with post holes has been excavated. This period is characterised by a production society which had mastered domestication and formed strong groups in the form of coastal villages principally oriented towards production related to fishing. Technologically, it was an innovating society, devising trifacial projectiles, fluting of certain points, sophisticated fishing kit, (shellfishhooks, big nets, shark-teeth, arrowheads, etc.). Fishing pearl is also attested in the Gulf and Arabian Sea. As an indication of new social relations, the creation of trade movement, especially over very long distances, is regarded as one of the characteristics of Neolithicization. In Arabia, it is during this period that complex networks of longdistance trade developed, internal to Arabia and reaching to distant lands such as the Horn of Africa. The materials traded in these networks included materials, such as exotic marine shells in the Rub Al-Khali and clastic rocks such as obsidian in Yemen and Saudi Arabia, and carnelian, agate and chalcedony in the Gulf, and possibly opalescent flint in the Oman peninsula. In the Emirates, it was this Neolithic population who made the first contact with the Ubaid 1 and 2-3 society, and were to assimilate goods and artificial materials (pottery, plaster, bitumen).

At about 4500-4200 BC, a new cultural entity emerges during a phase of great aridification and disappears about 3700 BC. Coming from the "trihedral points facies", its material culture is manifested by the appearance of several innovations, some of which affect the lithic industry: new forms of very slender projectile points, with an often fusiform silhouette and a diamond-shaped or lozenge-shaped section. Within the assemblage a true blade production is manifested, as much in Ja'alan as in Northern Oman and the UAE. Along the Arabian Sea, fishing equipment becomes standardized and new tools are henceforth fabricated. It is during this period, even a little earlier, that the open sea is conquered, with tuna fishing in the Sea of Oman and in the Arabian Gulf (cf. Dalma, Akab, Ras Al-Hamra RH-6, etc.). At Suwayh, this facies is present in all the late levels of SWY-1 and 20, in the earliest levels of SWY-2 and 3. The occupation at Ras Shaqallah SAQ-1, Ras Al-Hamra RH-6 and the earliest levels of Ras Al-Hamra RH-5 are related to this group, as are several sites of the Gulf (Al-Madar, Jazirat Al-Hamra and Ar-Ramlah 6).

In the Ja'alan, the sites attributable to the end of the Neolithic are the most numerous and those whose material culture we know best. More than fifty sites of this period were found, mainly on the coastal side, and several excavations or test trenches were made, at Ras Al-Hadd (HD-2.5, HD-6 Period I), Ras Al-Jinz RJ-2 (Period I), Suwayh (SWY-2, 3, 10), and Ras Al-Khabbah (KHB-1). ■

FIGURE 3

 3 FIGURE 3.1. Ras Al-Jinz 37 a 8 th millennium camp site during 1989 excavation (copyright, Y. Guichard).

FIGURE

  FIGURE 3.2. Ras Al-Jinz 37 during the 1989 season (copyright, V. Charpentier).

FIGURE

  FIGURE 3.3. Fasad point from BJD-1 Dandah Al-Jaddeed Al-Haddah, 8000-7500 BC (copyright, V. Charpentier).

FIGURE

  FIGURE 3.4. Trihedral point for Khor Al-Hajar KHJ-1, 6500-4500 BC (copyright, V. Charpentier).