Axel Baldanza
email: a.baldanza@rematch.fr

Jean-Franc ¸ois Aujol

Yann Traonmilin

Franc ¸ois Alary

Piecewise linear prediction model for action tracking in sports

Recent tracking methods in professional team sports reach very high accuracy by tracking the ball and players. However, it remains difficult for these methods to perform accurate real-time tracking in amateur acquisition conditions where the vertical position or orientation of the camera is not controlled and cameras use heterogeneous sensors. This article presents a method for tracking interesting content in an amateur sport game by analyzing player displacements. Defining optical flow of the foreground in the image as the player motions, we propose a piecewise linear supervised learning model for predicting the camera global motion needed to follow the action.

I. INTRODUCTION

Sports tracking is an important problem in computer vision because of the increasing demand from sports institutions or television channels for automatic algorithms. Such algorithms can be used to analyze player motions, game sequences or to make cameras able to record the game automatically.

Current state-of-the-art approaches for spatial or temporal action localization use detection of objects at the frame level [START_REF] Chao | Rethinking the faster r-cnn architecture for temporal action localization[END_REF], [START_REF] Singh | Online real-time multiple spatiotemporal action localisation and prediction[END_REF], [START_REF] Weinzaepfel | Learning to track for spatio-temporal action localization[END_REF]. The detected objects are linked or tracked across time to process the action localization in the video. In professional sports, high-definition cameras placed above the field make ball detection possible because the ball is less occluded and more recognizable in these conditions. The information of the ball position can then be used to track the action. [START_REF] Komorowski | Deepball: Deep neural-network ball detector[END_REF], [START_REF] Wang | Take your eyes off the ball: Improving ball-tracking by focusing on team play[END_REF], [START_REF] Yoon | Analyzing basketball movements and pass relationships using realtime object tracking techniques based on deep learning[END_REF], [START_REF] Yu | Trajectorybased ball detection and tracking in broadcast soccer video[END_REF] present adaptations of methods based on object detection at the frame level for tracking the action. These articles use players and ball detection to track the ball position. But in amateur sports, where the vertical position of the camera is variable from a game to another, and where the cameras use heterogeneous phone lenses, it is a more difficult task. For the same reasons, and because of the variability of ball appearance between different sports, other ball detection algorithms as D'Orazio et al. [START_REF] Tiziana | A new algorithm for ball recognition using circle hough transform and neural classifier[END_REF] would not be accurate in our model. We evaluated state-of-the-art neural network architectures for object detection on our test database. These architecture are used in [START_REF] Chao | Rethinking the faster r-cnn architecture for temporal action localization[END_REF], [START_REF] Yoon | Analyzing basketball movements and pass relationships using realtime object tracking techniques based on deep learning[END_REF] to detect balls or localize action across frames. The two models tested are a YOLO (You Only Look Once) architecture [START_REF] Jocher | Yolov5[END_REF], [START_REF] Redmon | You only look once: Unified, real-time object detection[END_REF] and a faster R-CNN (Region-Based Convolutional Neural Network) [START_REF] Massa | maskrcnn-benchmark: Fast, modular reference implementation of instance segmentation and object detection algorithms in pytorch[END_REF], [START_REF] Shaoqing Ren | Faster rcnn: Towards real-time object detection with region proposal networks[END_REF] with weights pre-trained on the COCO dataset [START_REF] Lin | Microsoft coco: Common objects in context[END_REF]. Both models managed to detect balls in less than 5% of the frames (respectively 2.12% and 4.81%). This justifies the need for a more robust tracking method dedicated to degraded acquisition conditions. In this paper, we propose a novel supervised learning approach for tracking interest zones in sports. We define interest zone as the area of the field a cameraman would have filmed. This necessarily includes tracking the ball, but does not have to always be centered in the image to make it more stable. State-of-the-art methods for motion prediction focus on predicting people or objects motion as Fernando et al. [START_REF] Fernando | Tracking by prediction: A deep generative model for mutliperson localisation and tracking[END_REF] who used motion prediction for multi-people tracking. Although predicting the motion of each person in the images can be a robust way to deduce a global motion, this kind of method is hardly usable in sports videos, where the player directions have sharp and unpredictable changes. Methods based on multi-view acquisition cameras as [START_REF] Li | Sift-based multi-view cooperative tracking for soccer video[END_REF], [START_REF] Poppe | Multi-camera analysis of soccer sequences[END_REF] can't be applied on our database because we dispose of only single view videos. To deal with these constraints, our method is based on predicting global motions of the zone of interest instead of local object motions. To predict the motion needed to track the action, we use a piecewise linear model learned on a database of amateur sport videos. Using this model, our method takes as input a sport video and returns a real number corresponding to the predicted camera motion at each frame. This motion is normalized as a percent of the total field. For this work, we used a basketball video database 1to train and test our model. As videos are captured by human beings, we assume these videos use a ground truth tracking of the action.

The main contribution of this article is the definition of an action tracking method based on a global motion prediction while other methods focus on object detection and tracking. The first main advantage of this new method is that it allows real-time tracking as it uses only fast operators. As presented in Dosovitskiy et al. [START_REF] Dosovitskiy | Flownet: Learning optical flow with convolutional networks[END_REF], optical flow can be calculated in real-time. The second main advantage of this method is that it avoids object detection which can be non robust with heterogeneous cameras and variable points of view. Finally, considering action tracking as a global motion estimation instead of localization allows us to annotate a large video database automatically, while labeling positions in videos is a time-consuming task.

II. OPTICAL FLOW BASED APPROACH

In this part, we describe a method based on the optical flow for deducing camera displacement. First, the method segments foreground and background. We assume that the background displacement corresponds to camera motion and we want to differentiate it from the foreground motions that we suppose to be the player motions. Warnakulasuriya et al. [START_REF] Romesh | Discovering methods of scoring in soccer using tracking data[END_REF] use player motions to predict team goals. This work induces that player displacements can indicate ball and action position. Following this intuition, player motions can be analyzed to predict the position or motion of the zone of interest. The estimation of a dense optical flow [START_REF] Liu | Beyond pixels: exploring new representations and applications for motion analysis[END_REF] yields a matrix of vectors (u i , v i ) resulting of the displacement of pixels in the image.

A. Background/foreground segmentation

Let us consider an image I as a R N vector. Players are defined as the moving foreground of the image. We assume that the background occupies more than half of an image. This is justified because sports cannot be captured close enough to make players occupy more than 50% of the screen without zooming. We define the background global motion at time t as the 2D median (u * , v * ) of the dense optical flow computed between the frames t and t -1

(u * , v * ) = argmin (u,v)∈R 2 N i=1 ||(u, v) -(u i , v i )||. (1)
with (u i , v i ) elements of the optical flow. (u * , v * ) is found by using iteratively reweighted least squares [START_REF] Paul | Robust regression using iteratively reweighted least-squares[END_REF]. We define the optical flow of the foreground f j ∈ R N ×2 as the optical flow matrix composed by elements distant to a threshold θ from the principal mode (u * , v * ) defined at equation [START_REF] Chao | Rethinking the faster r-cnn architecture for temporal action localization[END_REF] and where other elements are fixed to 0. To make the foreground values independent of the camera motion, nonzero elements of the foreground are added to (u * , v * ). f j is a vector of N components f j i defined as

f j i = (u i + u * , v i + v * ), if ||(u i , v i ) -(u * , v * )|| 2 ≥ θ. 0 else .
(2) As the threshold θ needs to be adapted for each frame, we propose to use

θ = λ N i=1 ||(u i , v i ) -(u * , v * )|| 2 N ( 3
)
with λ a constant manually defined to maximise the segmentation quality.

Figure 1 shows examples of background/foreground segmentation applied with this method. In the following, we consider only the horizontal component of the foreground optical flow for simplicity of notations because basketball camera displacements used in our examples are essentially horizontal. For other sports, the vertical component can easily be added to our model.

B. Environment normalization

This part presents optical flow normalization to increase the robustness of our model and to deal with the huge changes between the acquisition positions induced by the amateur conditions (position of the cameraman in the stands, distance to the field, ...). First, the lateral position of the camera is assume as known because the camera needs to be placed in the middle of the field to make our model consistent.

1) Scale: First, due to amateur conditions, the model needs to be robust to large changes in player size induced by variations of the distance between the camera position and the field. To avoid the impact of these variations, we define n f the number of activated pixels in the foreground and n b those activated in the background. We define η ∈ R as

η = n b n f α , (4)
where α ∈ R is a parameter used to adjust the impact of scale normalization on the prediction (fixed to 1.3 in our experiments). The scale normalization is defined as above because the prediction model defined in [START_REF] Fernando | Tracking by prediction: A deep generative model for mutliperson localisation and tracking[END_REF] depends on the activated pixel number in the foreground. If the camera is placed far from the field, we will obtain high values for η.

2) Vertical position and camera orientation: As images are taken from a single position, we cannot normalize camera placement with a full homography. In these conditions, we use a direct linear transform [START_REF] Dubrofsky | Homography estimation[END_REF] to normalize the camera position. Our model uses linear rescaling to normalize the impact of vertical position and camera orientation on the player appearance. As explained in the scale normalization part, our prediction model depends on the number of activated pixels in the foreground, and camera orientation can have a strong impact on player size. Depth is normalized by η. Linear rescaling is applied to the result of the segmentation f j . To determine the rescaling for each f j , we apply a 2 points vertical correspondence between the optical flow of the foreground and the normalized space. Figure 2 shows examples of environment normalization results on the foreground position. We see players are vertically replaced and the vertical wingspan is adjusted.

C. Motion prediction

Our model aims at deducing global motion needed to track action from the player motions computed in [START_REF] Tiziana | A new algorithm for ball recognition using circle hough transform and neural classifier[END_REF]. In this part, we present how our model is deducing global direction from segmented optical flow. The idea is to transform a complex action localization into a simple piecewise linear problem. The computational cost of linear prediction allows us to track the action in real-time.

We write d j ∈ R the camera displacement we want to deduce at time j from f j constructed as in equation ( 2). We can solve the problem by defining the linear model

d j = f j η, z + e j (5)
where z ∈ R N is a learned weight vector, e j ∈ R the prediction error and η the scale normalization parameter we defined in [START_REF] Dubrofsky | Homography estimation[END_REF].

During a video, the same player motions can induce different camera motions depending on the occurring situation. For example, all players running in a direction would require camera motion if it is located in an extremity of the field and not in the other one. According to this, our model has to be able to predict different motions depending on the situation for the same foreground optical flow.

We denote by s a situation and we extend the model ( 5) to the piecewise linear model

d j = f j η, z s + e j ( 6
)
where there is a different weight vector z s learned for each situation. In applications, the camera position is assumed known because of the calibration. The situation management can be deduced using the camera position. For evaluating the predictions on our data, situation management is done by analyzing the evolution of the ground truth values. The starting situation is annotated manually and situation changes are applied when the sum of ground truth displacements reach 100% as ground truth values are normalized in percent of the field as presented in the next part. The idea behind situations separation is to make the model adaptive to a maximum of different behavior. By defining adapted situations, this model is extendable to other sports and not only basketball.

D. Model learning 1) Labelization:

In this part, we present an automatic annotation method for our database. As explained before, our model predicts a global tracking motion by linear multiplication with a weighted learned matrix. To train the model and fit weight matrices z s defined in [START_REF] Paul | Robust regression using iteratively reweighted least-squares[END_REF], foreground optical flows need to be labeled with associated camera motion. This is done automatically by considering the global motion needed to track action as the horizontal component u * defined in (1) normalized as a percentage of the total field. Comparing the curves obtained with this method and video contents allow us to prove that the global computed background motion, defined as u * , is indeed associated to the camera behavior. Assuming that the sum of these displacements is representing 100% of the field, we can normalize each motion as a percentage of the total field. This allows the model to be robust to scale changes during the training because these variations can induce different background displacements for the same camera motion.

2) Situations and training: In this work, the database is split into two situations: action starting in the left side of the field (s = 0) and on the right side (s = 1). We trained the 2 matrices z r and z l for each situation by using ADAM optimizer [START_REF] Diederik | Adam: A method for stochastic optimization[END_REF]. To fit the model, the loss function is defined as

L(z s ) = ||F s z s -d s || 2 + 1 K i=1 Φ i (z s ) ( 7
)
where K is the batch size, F s is a matrix composed of K normalized foreground optical flow vectors, d s is a vector composed by the K camera motion associated labels. Φ i are penalization functions that favor a motion direction corresponding to each situation (motion to the right for s = 0 and to the left for s = 1 typical in basketball).

Φ i (z) = max((-1) s+1 F i s , z s , 0) 2 . ( 8
)
The learning rate is set to α = 10 -6 . The parameter is set to 0.1. It must be noted that the penalization Φ should be adapted to the sports considered with any prior knowledge for a given situation.

Finally, a post-processing step is performed on the predicted motion. This step is composed by a Gaussian smoothing and a thresholding to force little values to 0 and avoid the results to drift.

III. EXPERIMENTAL RESULTS

In this section, we study the effectiveness of our opticalflow based method to track interesting contents in basketball amateur games.

A. Dataset

The training database is made on 4050 optical flow vectors from 27 videos of 10 seconds computed of amateur videos. Videos from this database match the constraint that the camera is placed in the middle of the field to make our model consistent.

B. Tracker evaluations

Performances are evaluated on 2250 optical flows computed from 15 different videos from the same platform. Two different versions of our method are evaluated in the test section. A first version of the model with no penalization function during learning (NO PEN) and the model with the penalization functions (PEN) to justify the use of these functions. We also highlight the impact of the post processing step by giving the results of the PEN model without this post-processing (NO PP).

1) Evaluation metrics: To evaluate numerical results of the model, we use the mean absolute error (MAE) on predictions and integrated predictions (i.e. position with respect to the start of the video):

M AE = n i=1 |y i -x i | n ( 9
)
where n is the number of predictions, y i the prediction and x i the ground truth value.

Considering time integration of prediction results highlights the gap between the predicted camera location at time t and the position of the ground truth. We consider that when the MAE on integrated predictions (IP) is over 15%, the algorithm has lost the location of the action. Analyzing MAE on standard prediction allows us to see if predictions are locally close to ground truth. In good tracking results, this value enables us to understand if the predictions are locally the same as ground truth or if the tracking is done by error compensation. This metric shows if bad results are induced by local errors or global ones.

2) Evaluation results: As there is no out of the box method designed to predict global camera motion in sport videos, comparison with state-of-the-art methods is not easy with our metric. As explained in the introduction, we tested two stateof-the-art object detection methods to track the ball on the test database and they detect balls in less than 5% of the frames. With these results, predicted camera lost match thread in all videos of test database with camera motions. Evaluation results are summarized in Table I. First, results show that postprocessing improve prediction performances. The thresholding in the post-processing explains why the model is able to predict exactly the ground truth in video 11 where the camera is not moving. The two models have the same number of best following results but PEN has fewer videos where the algorithm is losing the match thread (MAE on IP >15%). This justifies the use of penalization during learning. According to the metric explained in the previous part and the perceptual analysis of the results, our method gives accurate prediction results on [START_REF] Poppe | Multi-camera analysis of soccer sequences[END_REF] I shows that a result has a MAE on integrated predictions >15%. In this case, we observe a non smooth camera displacement during player motion. This particular behavior generates the gap between predictions and ground-truth.

IV. CONCLUSION AND FUTURE WORKS

In this paper, we have presented an optical flow based method for following the action in an amateur sports game. Our method deduces global motion needed to track action from segmented optical flow by applying a piecewise linear operator. The main advantage of this method is that accuracy does not depend on the camera position or lens quality as it is the case for methods tracking the ball by detection. Moreover, the computational cost is smaller than for the ball detection based methods and it mainly depends on computing optical flow complexity. Data can be automatically labeled with the global motion of the background.

Our method shows some limits in its capacity to track very long match sequences. With our automatic labelling procedure, we are now able to construct a large database. A possible future work is to define a neural network architecture trained on such a database to predict motion. We can fit the network by using the model defined above to predict directions by analyzing optical flow vectors. Another way to improve the results is to combine detection based methods to this one to outperform the limits of each method.

Figure 1 :

 1 Figure 1: On the left column, images taken from a video. In the middle, optical flow computed from the left image and the previous frame. On the right, background/foreground segmentation.

Figure 2 :

 2 Figure 2: On the left, foreground/background segmentation in the starting space. On the right, foreground/background segmentation after linear rescaling.

Table I :

 I videos of the database. Examples of accurate Mean absolute error computed on simple predictions (MAE) and on integrated ones (MAE on IP) with the two versions of the model for every video in the database. The table shows that PEN is the best model on this database and gives good tracking results on 14 videos (MAE on IP ≤ 15). In this table, the values are normalized to percentages of the total field. Videos where MAE on IP ≤ 15% of the total field are considered as well tracked. tracking results in Table I are detailed in Figure3. These examples show samples where the model gives predictions close to the ground truth and where the action is precisely located. Graphs show that predicted curves are closely following ground truth. The blue rectangle in the images shows that the predicted camera is keeping the action on the screen. MAE computed on standard predictions shows that the model can compensate prediction errors across time. Looking at the left part of the table shows that local predictions can be closer to the ground truth but give integrated predictions less accurate. This is explained by compensation. Table

			MAE		MAE on IP
	Video	NO PEN PEN NO PP	NO PEN	PEN	NO PP
	1	0.01	0.01	0.22	1.03	0.10	2.21
	2	0.27	0.23	0.42	4.17	5.67	12.33
	3	0.72	0.86	1.09	10.26	13.70	22.05
	4	0.62	0.58	0.95	14.02	9.85	23.9
	5	0.32	0.33	0.46	15.27	11.41	14.77
	6	0.22	0.25	0.52	5.69	12.36	11.6
	7	0.45	0.55	0.70	4.71	4.72	5.91
	8	0.58	0.36	0.61	4.84	4.99	6.47
	9	0	0.11	0.58	0	3.58	24.12
	10	0.72	0.54	0.82	12.05	6.26	13.10
	11	0	0	0.15	0	0	2.70
	12	0.66	0.65	0.97	15.74	12	17.55
	13	0.98	0.86	1.07	24.58	18.57	23.33
	14	0.27	0.11	0.25	2.92	4.18	2.41
	15	0.35	0.41	0.57	8.40	7.01	9.97
				MEAN	9.29	7.62	12.23
				MAX	24.58	18.57	24.12
		NUMBER OF MAE >15	3	1	4

From Rematch platform: www.rematch.tv

ACKNOWLEDGEMENTS

This work was co-funded by Rematch Company, the Ministère en charge de l'Enseignement Supérieur, de la Recherche et de l'Innovation and ANRT who financed CIFRE theses. Figure 3: Examples of good tracking results by the algorithm in videos n°2,7,14 and 15 in the database.


Bruno Chianca Ferreira

Guillaume Dufour
email: guillaume.dufour@onera.fr

Guthemberg Silvestre
email: silvestre@enac.fr

Towards a Novel UAV Position Tracking and Reporting System for Very Low Level Airspace

Keywords: utm, uas, edge, emulation, ads-b, mobile, ad-hoc

The integration of Unmanned Aircraft Systems into the airspace is a challenging, complex task for both operators and regulators. To ensure a safe and secure UAS integration, they should rely on wide variety of dependable sub-systems, including a tracking and position reporting system. This paper proposes a system architecture for tracking and position reporting of UAS in very-low level airspace. The system leverages low-latency communications and distributed computing to offer highly available, consistent tracking information. Preliminary results suggest that our approach is especially useful for the traffic management and operations in densely populated areas.

Introduction

Recently, there has been increasing interest in Unmanned Aircraft Systems (UAS) for many real-life, civilian applications [START_REF] Shakhatreh | Unmanned aerial vehicles (uavs): A survey on civil applications and key research challenges[END_REF], including real-time monitoring, remote sensing, search and rescue, agriculture services and delivery of goods. In addition, a rapid growth in the number of drones in activity is expected, especially at very low-altitude of airspace with high demand in densely populated areas [START_REF] Undertaking | European drones outlook study[END_REF]. For instance, a recent study [START_REF] Rumba | The wild west of drones: A review on autonomous-UAV traffic-management[END_REF] forecasts that 98% of the aircraft operating in the airspace of Paris by 2035 will be autonomous. The integration of UAS will certainly result in fundamental changes of the air traffic management (ATM). Consequently, there is a need for the design of an Unmanned Traffic Management (UTM) system that will be able to manage a large number of autonomous vehicles in a safe and efficient manner.

One of the key components of the emerging UTM system is the the capability to track the vehicles' positions. Currently, tracking and position reporting of aircraft relies on long-range radio communications. Unfortunately, a large number of vehicles communicating through conventional radio frequencies (RF) in densely populated areas is likely to incur mutual interference and, consequently, poor performance. One way of reducing interference is to limit the range of the wireless radio but, which in conjunction with the limitation introduced by the buildings, it can render systems such as Automatic Dependent Surveillance-Broadcast (ADS-B) unfeasible. Furthermore, it remains unclear how the current ATM systems could be redesigned to enforce highly available, consistent position reporting to meet safety and performance requirements of novel UTM systems.

This study aims to investigate the feasibility of a novel tracking and position reporting system that could replace ADS-B in the context of UTM and UAS. The rational behind it is two-fold. First, the new system should allow small autonomous vehicles to communicate with low-cost, low-footprint, short range wireless interfaces and broadcast real-time data with local stations in the vicinity. Second, the system should rely on distributed computing techniques to share positioning data of vehicles with high availability and strong consistency, allowing even aircraft which are beyond line of sight to have updated information, ensuring proper functionality of their own applications. In this paper, we introduce a system architecture to reach the aforementioned design goals by deploying a distributed tracking and position reporting system throughout stations of Radio Access Network cloudlets, as depicted in Figure 1.

The architecture provides performance requirements, such as low-latency, high-throughput data exchange thanks to 5G's communication capability. To meet consistent, highly available positioning data sharing, our architecture leverages the functionalities of a strongly consistent distributed key-value store. Preliminary results based on mobile systems' emulation suggest that this architecture meets both performance and safety requirements of emerging UTM's tracking and position reporting system.

State of the Art

Unmanned Traffic Management

The rapid expansion of the market of small UAS has created new risks for civil aviation [START_REF] Lundberg | Urban Air Traffic Management (UTM) Implementation in cities -Sampled side-effects[END_REF] [START_REF] Rumba | The wild west of drones: A review on autonomous-UAV traffic-management[END_REF]. That increases the need for regulation and deployment of a fully functional UTM [START_REF] Elsayed | The impact of airspace regulations on unmanned aerial vehicles in last-mile operation[END_REF]. Some governmental agencies have been more prominent in UTM proposals, such as USA with NASA/FAA and European Union's SESAR/U-space. In [START_REF] Kopardekar | Unmanned aircraft system traffic management (UTM) concept of operations[END_REF], the author described NASA's research initiative related to the concept of operations (ConOps). NASA established a research platform which is used together with their partners to test and evaluate the challenges and solutions proposed for each of the technical capabilities associated with UTM. For NASA/FAA the UTM is set to evolve incrementally according to technical capability levels (TCL), and some research works have been conducted in order to verify the full development and verification of TCL levels. In [START_REF] Rios | NASA UAS traffic management national campaign: Operations across Six UAS Test Sites[END_REF] flight tests demonstrating the most basic TCL levels 1 and 2 were performed even with beyond visual-line-of-sight (BVLOS) for unpopulated areas. BVLOS in populated areas is introduced in [START_REF] Rios | Flight Demonstration of Unmanned Aircraft System (Uas) Traffic Management (utm) at Technical Capability Level 3[END_REF], where the authors performed a flight demonstration of TCL3. In [START_REF] Chakrabarty | Autonomous flight for multi-copters flying in UTM -TCL4+ sharing common airspace[END_REF] the author demonstrates TCL4 capabilities using simulation tools, and gave a high emphasis in safety by describing in details the SAFE50 architecture.

The framework on how a UTM system should work and the interaction between the stakeholders is not yet finalized [START_REF] Mccarthy | Fundamental elements of an urban UTM[END_REF] and many aspects are not clear in order to achieve the highest levels of autonomy. However, the main proposed architectures are composed of distinctive applications [START_REF] Labib | A multilayer lowaltitude airspace model for UAV traffic management[END_REF] such as sense and avoid [START_REF] Scott | Distributed bidding-based detect-and-avoid for multiple unmanned aerial vehicles in national airspace[END_REF][START_REF] Minucci | Avoiding Collisions at Any (Low) Cost: ADS-B like Position Broadcast for UAVs[END_REF][START_REF] Park | Unmanned Aerial System Traffic Management with WAVE Protocol for Collision Avoidance[END_REF][START_REF] Lin | Sense and avoid for unmanned aerial vehicles using ads-b[END_REF], path planning [START_REF] Besada | Drone flight planning for safe urban operations: UTM requirements and tools[END_REF][START_REF] Tan | Evolutionary optimization-based mission planning for UAS traffic management (UTM)[END_REF][START_REF] Sujit | Multiple uav path planning using anytime algorithms[END_REF][START_REF] Chakrabarty | Real-time path planning for multi-copters flying in UTM-TCL4[END_REF], which rely on the fact that trustable data can be shared among stakeholders with low latency.

Aircraft Surveillance

A position tracking and reporting system is a crucial system for aircraft surveillance. The Automatic Dependent Surveillance-Broadcast (ADS-B) is a service present in aircraft 4 that broadcasts relevant unencrypted data in real-time. It aids radars in keeping updated and correct information about all the aircraft currently flying. With such information about all aircraft, air traffic management (ATM) authorities can develop applications to improve security, and efficiency of air transportation system and airports. Albeit not mandatory like ADS-B Out, other aircraft can also receive broadcasts with ADS-B In and use the information to build knowledge about its surroundings in order to improve conflicts avoidance. Aircraft equipped with ADS-B equipment, periodically broadcast their call sign, latitude and longitude, ground speed and flight number with signals modulated in 1090 MHz. Considering the importance systems like ADS-B have for ATM, a similar technology is also expected to play an important role in UTM. Unlike large aircraft, small UAVs are harder to be detected with radars, increasing the importance of a ADS-B like system. Previous works have proposed ADS-B alternatives in the context of UTM as explored in [START_REF] Orrell | Small unmanned aircraft system (SUAS) automatic dependent surveillance-broadcast (ADS-B) like surveillance concept of operations: A path forward for small UAS surveillance[END_REF]. The authors in [START_REF] Lin | An ADS-B like communication for UTM[END_REF] and [START_REF] Lin | ADS-B Like UTM surveillance using APRS infrastructure[END_REF] proposed an architecture based in low-cost radio transferring data to a central cloud, which does not solve the problem of fast replication across the urban area for low latency and availability to all stakeholders. In [START_REF] Lin | ADS-B Like UTM surveillance using APRS infrastructure[END_REF] the author proposes an ADS-B like system for UTM based on APRS (Automatic Packet Reporting System), which is an approach different to what is proposed in this work, since it is based on relatively long range radio (40Km) with restricted throughput. In [START_REF] Minucci | Avoiding Collisions at Any (Low) Cost: ADS-B like Position Broadcast for UAVs[END_REF], the author proposed a solution to inject the position data in the SSID of WiFi and the results has shown that the proposed setup yielded reasonably low latency (under 125 ms) and acceptable throughput (4 messages/s) under an experimental setup. By having a secure ADS-B like data layer, applications such as presented in [START_REF] Lin | Sense and avoid for unmanned aerial vehicles using ads-b[END_REF] where the authors proposes a sense and avoid system that used ADS-B data as input, can be built.

A Novel System Architecture for Tracking and Position Reporting

Our system architecture is designed to enable fault-tolerant and efficient data sharing for UTM stakeholders. The main blocks of this architecture are shown in Figure 2. It is built on top of two key components: a distributed, strongly consistent key-value store and the next-generation cellular communication technology. The distributed key-value store is composed of distributed UTM Data Service (UDS) units spread across the urban area as shown in Figure 1. We assume that UDSs are deployed in federated cloudlets interconnected through low-latency mobile network, such as 5G or 6G [START_REF] Azari | Evolution of Non-Terrestrial Networks From 5G to 6G : A Survey[END_REF]. In this section, we describe the design of our architecture by focusing on the SMR protocol and the architecture's API endpoints. We skip further details about the mobile network due to space constraint.

State Machine Replication

To enable fault-tolerant, highly available key-value store, UDSs run state machine replication (SMR) protocol [START_REF] Schneider | Implementing Fault-Tolerant Services Using the State Machine Approach: A Tutorial[END_REF]. SMR is a technique to implement faulttolerant service by replicating servers and coordinating client interactions with server replicas. In particular, stakeholders (e.g., service providers, operators and vehicles) are clients and servers/replicas are UDSs. Our architecture leverages Fig. 2: Our System Architecture etcd5 , a distributed, strongly-consistent key-value store, to run SMR. This distributed approach solves important problems of ADS-B [START_REF] Kim | ADS-B vulnerabilities and a security solution with a timestamp[END_REF], such as lack of fault tolerance, data inconsistency, and unpredictable availability of shared data.

API Endpoints

The API endpoints are used to put or get data from the system.

-ADS-B Transponder -A ADS-B receiver connected to the system can put data from aircraft. -Service Endpoint -The end-point that can be used by the UTM service providers or operators to get the current and past state of the airspace via restful API, time series or stream. -UAS Endpoint -Used by UASs to insert broadcast data into the system.

Experimental Evaluation

This section presents the performance evaluation of our system architecture using MACE [START_REF] Ferreira | Mace: A mobile ad-hoc computing emulation framework[END_REF], an emulation framework to study, design and evaluate mobile Adhoc applications. Figure 3 shows the architecture of our emulation with MACE detailing how the main blocks communicate with each other.

Cloudlets and Aircraft

MACE uses CORE as network emulator, and it emulates each network instance as Linux namespaces serving as minimal containers. Each aircraft client application runs inside these namespaces, and they communicate via veth network interfaces with connectivity controlled by the distance between the nodes. The cloudlets are also emulated in such namespaces with a server running the UAS endpoint and interfacing instances of etcd running in the same namespaces. The emulated scenario is run over an area of one square kilometre.

Mobility

The Random Waypoint mobility model was adopted for the experiment. In this model each aircraft receives a random waypoint and a random velocity to simulate a mission's objective. The movement of the aircraft is emulated in MACE, and the real-time position is injected directly in the network emulator so that it is reflected in the network connectivity. The position is made available to the applications running in the virtual aircraft via UNIX sockets.

UAS Broadcasts

For the payload reporting, a client running in each aircraft broadcasts a JSON object containing the position and additional data via IPV4 UDP sockets using the emulated Ad-hoc wireless links. The payload includes also an unique message ID, timestamp, an aircraft ID, velocity and status. The unique message ID is used to verify that the message was received and the timestamp used to calculate the latency between the broadcast and full replication.

UDS Cloudlet

To simulate the UDS cloudlets, a server representing them is deployed in each emulated cloudlet. The servers which are in range of a broadcasted message, will receive the new data in the UAS endpoint and replicate it to the other towers which are not in range by using the state machine replication layer. Data is also written in persistent storage for posterior analysis. The consistent replication ensures that the data is reliable across all participant cloudlets, so that distributed third part actors can see this reporting system as a trusted oracle for UTM applications such as asset managers, schedulers and collision avoidance path planners. When a message is fully replicated among all replicas, a callback function records the time stamp so that the total latency can be calculated.

All the experiments were performed on a Linux server whose configuration is described in Table 1. Our empirical evaluation is split in the scenarios detailed in Table 2.

Preliminary Results

In the first scenario, the main goal was to measure the latency between the data broadcasting and full replication when there are no network losses between cloudlets or in the UAS communication interfaces. One of the side effects of the strong consistency is the communication complexity consequence of the multistep consensus algorithm. So, in addition of the broadcast latency, it is expected also a component for the replication latency.

We assume that ADS-B broadcasts 2 messages per second since detect and avoid / path planning algorithms usually run with frequencies ranging from 1Hz to 2Hz. A previous experiment with only one fixed UAS was run to measure the replication overhead. Running such scenario yielded an replication overhead of 10ms, which is acceptable but is closely related to the number of replicas and, more considerably, to the total coverage area. Larger areas would require more communication hops even if the number of replicas is left unchanged, hence increasing the total latency. The impact of the introduction of losses is perceived differently in the UAS links and intra-cloudlets links. Since in this implementation the UAS broadcasts data via UDP links (more suitable for mobile and lossy links), lost messages do not impact the broadcast latency because there are no timeouts and retransmissions. Since etcd is implemented to communicate via TCP, the losses increase the overall replication latency as shown in the Figure 4. It is important to notice in Figure 4(b) that increasing the number of aircraft while leaving the delay between broadcasts low increase significantly the end-to-end latency. This could mean that in order for such platform scale to more representative scenarios of a crowded airspace, the number of replicas cannot be too high. It is also important to highlight that since these were performed with an emulator, all software components related to all cloudlets and UAS, such as the clients, servers and etcd, are running in the same computer competing for resources, and that the its state can affect the results. It is therefore unfeasible to emulate scalability tests on an emulation platform, since they consume too much computer resources, and more tests with a simplified replication model running on a scalable simulator are required.

5 Discussion, Limitation and Future Work

The emulator helped us to implement and evaluate a very first prototype of our proposal, providing quick, yet preliminary results. For instance, latency measurements with many applications running on a single computer might skew the results. The server implementation (i.e., an UDS unit) used a callback function from a etcd library that was not designed to have low-latency capability, specially when running multiple requests simultaneously. In this preliminary study, we also overlooked the impact of the number of replicas in the overall latency while keeping a large number of access points. We also ignored the impact of different failure models, including a Byzantine one. One important aspect of such deployments is how they will act in presence of malicious actors, which is a reasonable assumption for a open air platform with competing actors. We believe that the target system could tolerate attacks such as Sybil attacks [START_REF] Yu | Detecting Sybil attacks in VANETs[END_REF]. Alternatively, we could consider a distributed data store based on blockchain technique in order to cope with Byzantine faults. For future work, scenarios with larger areas, different number of replicas are required. This would ensure a more clear view of the latency impact of the replication quorum. Furthermore, scalability studies are also required to simulate scenarios with hundreds of UAS. A fast simulator would also allow the study of optimal placement of such replicas in different realistic maps.

Conclusions

This work presents a novel tracking and position reporting system to enable emerging UTM services for autonomous vehicles operating at very low level airspace. Our preliminary performance evaluation suggests that the latency measurements yielded results that are suitable for building a system architecture for UTM in densely populated areas. The highly available, distributed data store allows even vehicles that are hidden behind constructions to be spotted by all stakeholders in a consistent way. In contrast to the current ADS-B, our architecture enable fast, fault-tolerant data sharing by design.

Fig. 1 :

 1 Fig. 1: Distributed UTM Data Service

Fig. 3 :

 3 Fig. 3: Emulation Architecture

(a) 10 Fig. 4 :

 104 Fig. 4: Total replication latency with increasing broadcast delay

Table 1 :

 1 Test Platform

	Processor Manufacturer / Model: Intel i7-8550U @ 4GHz
	Number of cores	8
	Memory	16GB DDR4
	Emulator	MACE
	Operating System	Linux Mint 20 x86 64bits
	Routing Protocol	B.A.T.M.A.N IV

Table 2 :

 2 Emulation Scenarios

	Setting	Without Losses	With Losses
	Cloudlet Range	250m	250m
	Number of cloudlets	4	10
	Cloudlet Bitrate / Delay 433.3Mbps / 1000us 433.3Mbps / 1000us
	UAS Range	90m	250m
	Number of UASs	5 and 20	5 and 20
	UAS Bitrate / Delay	54Mbps / 3000us	54Mbps / 3000us
	Jitter	0 us	2 us
	Error rate	0%	1%

Mandatory in many countries depending on aircraft weight or airspace class.

https://etcd.io/


TaPAS : The Talence Presburger Arithmetic Suite

Jérôme Leroux and Gérald Point LaBRI, Université Bordeaux 1, CNRS.

{leroux,point}@labri.fr

Abstract. TAPAS is a suite of libraries dedicated to FO (R, Z, +, ≤). The suite provides (1) the application programming interface GENEPI for this logic with encapsulations of many classical solvers, (2) the BDD-like library SATAF used for encoding Presburger formulae to automata, and (3) the very first implementation of an algorithm decoding automata to Presburger formulae.

The Mixed Additive Theory

The automatic verification of reactive systems is a major field of research. These systems are usually modeled with variables taking values in some infinite domains. Popular approaches for analyzing these models are based on decision procedures adapted to the variables domains. For numerical variables the mixed additive theory FO (R, Z, +, ≤) provides a natural logic to express linear constraints between integral variables and real variables. This logic has positive aspects: it is decidable and actually many solvers implement decision procedures for the full logic or some sub-logics like the Presburger arithmetic. TAPAS is a suite of libraries dedicated to these logics. The sequel is organized as follows. In Section 2 the architecture of TAPAS is presented. Section 3 presents the BDD-like library SATAF used for encoding Presburger formulae to automata and for decoding automata to Presburger formulae. Finally, Section 4 provides some benchmarks.

TAPAS at a Glance

The following figure shows the architecture of TAPAS (enclosed by the dotted line). The FAST model-checker is also depicted but it does not actually belong to the suite; it is just a client application. Selecting the most efficient solver for a given application can be difficult. This choice can change dramatically the practical performance of the application. Since solvers have incompatible application programming interfaces (API), a particular one must be first selected prior the implementation of the application; change afterward require additional development effort. The GENEPI library [START_REF] Bardin | Fast extended release[END_REF] addresses this issue by offering small APIs between, on one side, applications requiring solvers and, on the other side, solvers implementing decision procedures. The connection between applications and solvers is realized transparently using dynamically loaded modules (plugins) specified at the execution time. This way the choice of a solver can be postponed after the implementation of an application based on GENEPI; the best one can be selected by performing benchmarks. Since [START_REF] Bardin | Fast extended release[END_REF], GENEPI has been enhanced with new features: support for R, new plugins (LIRA and PPL), . . . In general, specifying sets with low level logics is difficult and fastidious. The same problem appears with FO (R, Z, +, ≤). The ARMOISE language allows to describe concisely sets of vectors (in Z and/or R). The succinctness of formulae is achieved using, among other tricks, hierarchical definitions and arithmetic over sets (which hides numerous and ugly quantifications). Below is an example of an ARMOISE formula which specifies a repeated pattern in N 2 . Note that ARMOISE formulae may define sets which are not necessarily definable in FO (R, Z, +, ≤). TAPAS provides tools to support the ARMOISE language. The ALAMBIC library permits to compile ARMOISE formulae into calls to GENEPI functions. An important step in this compilation process is the translation of high-level constructions into the mixed additive theory; due to the expressive power of ARMOISE this transformation is not always possible.

SATAF: Shared-Automata And The Synthesis of Formulae

Many solvers like LASH, LIRA and MONA are based on automata packages. Intuitively, mappings from words to numerical vectors are used to associate to automata potentially infinite sets of numerical vectors (one vector per accepted word). Usually, the minimal deterministic automata are proved canonically associated to the represented sets and not on the way they have been computed. In particular these solvers are well adapted to sets obtained after long chains of operations like in symbolic model checking. In [START_REF] Couvreur | A bdd-like implementation of an automata package[END_REF], Couvreur introduced a new data-structure called shared-automata. Intuitively, the sharing of a finite set of automata is performed by merging every states equivalent with respect to the Nérode relation. TAPAS contains the SATAF library that implements this data structure. In SATAF, deciding if two automata recognize the same language reduces to check the equality of their pointers. Similarly to BDD packages, SATAF uses a pointer-based hash-table cache algorithm. Up to our knowledge, no other automata package implements these features. Since the first version of SATAF written in JAVA by Couvreur [START_REF] Couvreur | A bdd-like implementation of an automata package[END_REF], a new version written in C is now maintained in TAPAS. TAPAS also provides an implementation of the GENEPI API based on SATAF. Extracting geometrical properties (for instance linear constraints) from automata is a challenging problem. From a theoretical point of view, this problem has been solved in [START_REF] Leroux | A polynomial time presburger criterion and synthesis for number decision diagrams[END_REF]. This article provides a polynomial time algorithm for computing Presburger formulae from automata representing Presburger sets. The algorithm first extracts the "necessary" linear constraints from the automaton. Then, it computes an unquantified Presburger formula using only these constraints, Boolean operations, translations by integer vectors, and scaling by integer values. An implementation of this algorithm is provided with The generated formulae follows the ARMOISE syntax. Note that SATAF, GENEPI and ALAMBIC provide together the very first implementation of an algorithm that normalizes Presburger formulae into unique canonical forms that only depend on the denoted sets. Intuitively in the normalization process, the minimization procedure for automata acts like a simplification procedure for the Presburger arithmetic.

Experimenting The Automata to Formulae Algorithm

FAST [START_REF] Bardin | Fast extended release[END_REF] is a tool for verifying reachability properties of infinite-state systems. The tool is implemented over TAPAS. Benchmarks of FAST on various GENEPI implementations are available in [START_REF] Bardin | Fast extended release[END_REF][START_REF] Becker | Lira: Handling constraints of linear arithmetics over the integers and the reals[END_REF]. We experimented the computation of ARMOISE specifications from SATAF automata denoting the reachability sets of 40 systems. Some results are presented in the following table. Column "→ A" is the time in seconds spent for computing an automaton A representing the reachability set, "|A|" is the number of states of A, "A → S" is the time in seconds to produce an ARMOISE specification S from A, |S| is the number of characters of S, "n" is the number of variables of S, and "l" is the number of linear constraints generated in S. We also experimented the normalization of ARMOISE formulae on various examples. Due to space limitation, only four representative examples are presented: modulo, large-coef, large-var and unsimplified. Example modulo denotes the Cartesian product (11N) × (7N) × (5N) × (3N) where mN is the set of non-negative integers multiple of m, large-coef is the conjunction of three linear constraints with coefficients larger than 20, large-var is a linear constraint defined over 36 variables, and unsimplified is a disjunction of two sets of linear constraints with redundant constraints. Benchmark results are summarized in the following table. Columns have the following meaning: "example" provides the name of the ARMOISE specification S 0 , "|S 0 |" is the number of characters of S 0 , "S 0 → A" is the time in seconds to produce a SATAF automaton A from S 0 . The other columns have been defined previously. We observe that the computation of SATAF automata A from ARMOISE specifications S 0 takes less than 2 seconds. Moreover, the computation of ARMOISE specifications S from A takes less than half a minute even on automata with more than 10 5 states. In practice the implementation (quadratically) slows down in presence of modular constraints. Note that |S 0 | < |S| in all our examples due to non-optimized outputs. However, even if |S 0 | < |S| in the last example unsimplified, the redundant linear constraints of S 0 no longer appear in S.

Contrary to previous results, we observe that |S| is quite smaller than |A|. Recall that the generated ARMOISE specifications are combinations of linear constraints. In both series of benchmarks formulae contain a few number of constraints (see the "l" column). The complexity of the combinations explains the differences in the results. In practice, we observe that small automata can encode complex combinations but only a small number of linear constraints.

Conclusion And Future Work

TAPAS is distributed at http://altarica.labri.fr/wiki/tools:tapas: under GPLv2. Thanks to GENEPI, this is the first tool to our knowledge which offers (1) a simple framework for the development of applications requiring solvers for the mixed additive theory and (2) an easy way to benchmark solvers. TAPAS also provides the SATAF solver based on shared-automata and the first implementation of the algorithm translating them into equivalent ARMOISE formulae.

Future Work. Predicate abstraction methods are limited by the number of considered predicates. Usually some of these predicates are redundant. More precisely, some predicates are not semantically used even if they syntactically appear. In future work, we are interested in using the normalization procedure of TAPAS in order to remove redundant predicates. In fact, the set of extracted linear constraints from an automaton is known minimal : these constraints syntactically appears in any unquantified Presburger formula that denotes the set represented by the automaton.

  let origin := (7,3); directions := { (4,0), (0,4), (4,4) }; pattern := ([0...2], [0...2]) \ (1,1); in origin + nat * directions + pattern;


Pascal Engel

Ruth Barcan Marcus

Is identity a functional property?

Introduction

The very first article authored by Ruth Marcus that I read, in 1977, was "Extensionality" (1960). 1 It awoke me from my Quinean dogmatic slumber, because it explained that extensionality is not limited to the domain of extensional logic and because it showed how one could construct a range of various notions of extensionality of different strengths, including for intensional contexts. It also seemed to me a remarkable example of how a philosopher and logician can construct a concept, whereas at the same time my teachers at Ecole normale supérieure were explaining to me that every concept had to be de-constructed with no hope of rebuilding. 2 In the same article Ruth Marcus examined the notion of identity and explained that the principle of the identity of indiscernibles (Id ind) (x) (y) ((Fy  F x)) → ( x = y ) ) could also be weakened (to be distinct means to be discernibly distinct) . She also hints, at the end of her article that when the statement "involves only proper names", then replacement of the "Morning star" by "the evening star" in such statements as It is necessary that the evening star is the morning star yields no paradox such as Quine's on the number of planets. It is clearly related to her theorem about the necessity of identity, which she established in her pioneering paper of 1946, and it anticipates the famous discussion of necessary identity statements with proper names in "Modalities and Modal languages" (1962) 3 .

It is this topic of the nature of identity, and of its possible variations, which I want to take up here. Traditional debates about the nature of identity bear upon whether it can really be a formal property or relation of objects, given that not all of the classical logical principles of identity seem to be formal at all. This has led philosophers to propose various non classical notions of identity and in particular to relativise the concept. But these attempts meet strong objections. I want here to examine another proposal. It has been suggested that truth could be a functional property, defined by its role, multiply realised in various domains. Can identity be considered as a functional property? The proposal would have the advantage of avoiding relativism about identity. But could it work? I argue that it can't and that we have to stick to our classical absolute concept.

Absolute identity

The difficulties of the classical definition of identity are discussed by Ruth Marcus in her essay "Possibilia and possible worlds" in the context of a discussion of the nature of possibilia (1986, 1993:189-213). Identity is taken to be a logical notion characterisable by the properties of reflexivity, symmetry, transitivity, indiscernibility, and substitutivity):

(R) (x) (x = x) (S) (x) (y) ((x = y) → (y = x)) (T) (x) (y) ( z) (((x = y) & ( y = z)) → ( x = z)) (Ind Id ) (x) (y) ( x = y ) → (Fy  F x)) (Id ind) : (x) (y) ((Fy  F x)) → ( x = y ) )
It seems to be the best way to define objecthood, and a primitive notion: « Identity is the strongest equivalence relation that a thing bears only to itself. That there are individuals is already presupposed if the identity relation is to hold. The identity relation does not confer thinghood; identity is an essential feature of things. Individuals must be there before they enter into any relations, even relations of self-identity. Of course if we want to discover which objects a language or theory takes to be individuals, we look to see which objects are such that they can meaningfully enter into the identity relation.

Quantification is not so clear a guide to ontology as is identity. No identity without entity." 1993 : 200) The problem, however, as Ruth Marcus reminds us, is that identity is not so clear, and that its definition in terms of indiscernibility (Id Ind above)things are identical when they have all their properties in common-encounters familiar problems: what does it mean to say that two things have all their properties in common? What kinds of properties are involved (qualitative or relational, including the relation of identity itself?)? The principle of the identity of indiscernibles cannot be fully logical or formal, for indiscernibility cannot define identity without further metaphysical assumptions.

There are indeed different criteria of the formal. Quine could not accept the necessity of identity as a formal property of it, except in the de dicto sense. But as Ruth Marcus remarks, for instance in her "A Backward Look at Quine's Animadversions on Modalities" (1988;1993: 229) andin "Essentialism in Modal Logic" (1967;1993: 50), the necessity of identity does not need other kinds of essential properties than self-identity, and is committed only to an innocuous form of essentialism. So there is a good ground to accept the necessity of identity among the formal-logical properties of identity. The situation is less clear with the non vague character of identity, which has been defended by Gareth Evans on the basis of a famous argument which is reminiscent of Marcus's proof of the necessity of identity (Evans 1982) 4 . A lot of discussion has been devoted to whether identity statements can be vague or not, but it seems difficult to deny that the property of an object to be self-identical could be vague. So there is good ground for adding to the classical list of formal features of identity (reflexivity, transitivity, indiscernability, substitutivity) those of necessity and non vagueness. All these make identity an absolute relation, which holds of objects independently of what kind of objects enter within the relation. In other words absolute identity characterises identity as a formal property in the sense that it is supposed to apply to any kind of object, whether it is physical, biological, mental, natural, artefactual, etc. Any two objects, if they are identical, are identical simpliciter, and not relative to any kind or sort. From Leibniz's law of substitutivity one can derive from (2)and (4):

(5) ~ (a=b) which contradicts the initial hypothesis that the identity statement 'a=b' is inderterminately true.

On Evans' argument, see Williamson 1994: 253-56, and the references thereof. See Also [START_REF] Engel | The Problem of the Morning Star and the Evening Star[END_REF] In he same article (1993: 228) Ruth Marcus notices that for Aristotle, essential properties are sortal, in contrast to trivial properties such as being an entity and being selfidentical. It is precisely because they have wanted to include within the property of being identical sortal properties that some philosophers have attempted to relativise identity itself to sortals. Geach (1972) claimed that the absolute concept of identity does not fit our usual way of asking identity questions. When we ask whether one object is identical to another, we never ask whether they are identical simpliciter, but we always ask questions of the form: "What kind of thing is x?" and we always reply, in the Aristotelian mode, that x is an F, or G, etc. When we ask whether x is identical to y, it is always relative to a sortal F,G, etc. This is, in a sense, how it should be, since the formal properties of identity (reflexivity, Actually a majority of problems which are called "problems of identity", those which give rise to famous paradoxes (material composition vs form, identity over time, Theseus' ship, the problem of the many, etc.) are problems relating to individuation. Take for instance Geach's case of the cat Tibbles as an illustration of "the problem of the many". 5Tibbles is a cat. Let us supose that he looses his tail, the resulting object being Tib. Tib differs from Tibbles. But Tibbles minus his tail coincides with Tib. And if Tibbles is a cat, Tib is a cat too. One can say that Tib differs from Tibbles as an individual but is identical to Tibbles as a cat. Aren't there two Tibbles? A variant has Tibbles lossing his hair on the carpet: if Tibbles looses 1000 hairs, 1000 Tibbles are on the carpet.

According to Geach, most of these paradoxes show that the predicate of identity, if it is to make sense within ordinary contexts, has to be relativised. « a = b » has always to be understood as (R) a is the same F as b where «F» is a sortal predicate. The problem, as David Wiggins has shown, is that relative identity (R) is incompatible with the principle of the identity of indiscernibles6 . The dilemma is: either identity is absolute, but it can't really be a relation into which ordinary objects enter, or it is relative, but then it ceases to be a genuinely formal relation.

Geach's problem about relative identity and the issues raised by the paradoxes of identity show that there are is a sharp contrast between what logic tells us about the identity relationwhich is absolute, simple, and necessaryand our identity judgmentswhich are relative, context-sensitive and contingent. Geach is right that in many contexts we do not ask whether a thing is identity to another simpliciter. Very often we satisfy ourselves with vague or loose identity statements ( "This is the same food as the one I had in another restaurant") or ambiguous ones ( for instance we are happy to accept certain type identity statements although we would reject their token counterparts : "This is the same train as the one I took for Arezzo last year"), and we rarely care for what Thomas Reid called the "strict and philosophical sense" of identity in opposition to its "loose and popular" sense (we almost never ask : "Is it really the same food as the one from the other restaurant ?", or " Is it the very same train as the one you took for Arezzo last year?"). In such cases, identity is neither absolute nor transitive, and seems akin to a notion of similarity. But can we content ourselves with the observation that there is a conflict between the loose and ordinary sense on the one hand and the strict and philosophical sense on the other?

The notion of an identity judgement is clearly person or context relative, as well as it is an epistemic notion. The difference between identity judgements from one context to another are obviously differences about the epistemic criteria by which we judge one thing to be identical to or to differ from another, or differences about our epistemic interests in asking identity questions. But identity questions are not epistemological questions: they are questions about what things are and their nature. But even if we understand these questions as ontological questions, the problem of the variety of identity questions still arises. When we ask whether a marble statue seen in the Acropolis museum in Athens is the same as one in plaster seen in a tourist shop in the Plaka below, we wonder about a difference in constitution. When we ask whether Theseus' ship at one time is the same as a ship of the same shape at another time, we wonder about a difference in material composition. These are principles about the individuation of entities, in an objective, and non mind-depend sense. But these questions about individuation differ from identity questions "strictly" speaking. But we cannot rest content with the thought that questions about identity are distinct from questions about individuation. We want to know how they are related. Does individuation depend on identity or vice versa?

Wiggins' individuative essentialism

Wiggins 20017 proposes a way out. He holds that any entity has to conform to the formal principles of the absolute concept, which are norms for specific issues about individuation which occur in various contexts and relative to various purposes that we have of classifying objects into kinds. Without these principles, no judgement to the effect that x is identical to y can make sense. According to Wiggins, however, it does not follow from this that attributions of identity are independent of the implicit reference to some sortal or other. Although identity is absolute, "the sortal dependency of individuation" still holds.

According to Wiggins' « individuative essentialism » it has to be true both that:

(1) Identity is absolute and defined by its formal properties ( R, S, T, ind Id, Id ind) 2. A thing x is identitical to another y if and only if there is a sortal concept F such that x and y fall under F 3. This concept provides the individuation of the entities in question and is a principle of coincidence and of activity, of functioning an operation ( in other words it is a substance concept (Wiggins 2001 : 72-73) According to this conception, individuation is relative to a common sortal concept which underlies any individuation, but this concept is left unspecified by the schema of the theory. It many be any sortal concept which is general enough to track the object. But this sortal concept does not vary from context to context, from one identity question to another.

On the contary the same sortal is presupposed by any individuation. It is the concept of what Wiggins calls a "continuant". Such a view seems equipped to answer some of the paradoxes about identity, such as the problem of the many. Confronted with the Tib-Tibbles case, individuative essentialism will say that Tib and Tibbles are two distinct entities which coincide under the same sortal (cat). Wiggins rejects any view which would say that Tib and Tibbles are composed of distinct spatio-temporal parts. Their difference is based upon their constitution. Although identity is a stable property, there are variations in the conditions of persistence, which differ according to whether one deals with material objects, biological organisms, persons, artefacts or different kinds of entities. Each one of these that its own individuative kind, but continuants falling under these kinds have distinct persistence conditions. Constitution does not definie identity, but identity supervenes on constitution. Identity is any relation which conforms to the formal principles (R), (S), (T), (id ind), (ind id), but for each kind of entity, there is a substantive account of the individuation of members of that kind, and conformity to the formal principles is a consequence of that account.

But can Wiggins' individuative essentialism solve our problem? If persistence conditions vary with the kind of entity involved in each case, and if identity surpervenes on persistence conditions, how can we escape the conclusion that identity is nothing over and above the constitution of the kinds? Do the formal principles hold in the same way in all domains? For instance if we accept that the constitutive principles for personal identity are based on a notion of psychological continuity of the Lockean or Parfitian kind, will identity be transitive ? Presumably not, for this depends upon whether psychologiucal continuity involves a strong or a weak form of continuity 8 . Can't we accept that the principles of individuation of some entities, such as social groups like clubs or associations, can be vague (a club does not cease to exist if it loses one of its members, but a loss of ten members may be fatal, where does the limit falls?). Do the formal principles of identity hold in basics physics? A number of writers hold the view that in quantum physics the identity of indiscernibles fails as well as the principle of the non vagueness of identity. 9 Similarly for biological entities 10 . The individuation conditions of an organism depend upon persistence conditions which differ from those of physical objects, artefacts or persons. These conditions are those which guarantee the continued process of the life of the organism.

But things are not so clear at the beginning of life: for instance the possibility of monozygotic twins suggests that a zygote is not a single and coherent life, but a system which has the potential capacity to form several lives. Hence in what sense are we confronted with a coherent whole or with a set of autonomous cells? The individuation conditions are not clear either at the end of the life of (human) organisms: medical practice has replaced cardio-pulmonary death with cerebral death. Should we then say that the irreversible loss of cerebral functions constitutes the death of the person or that of the organism? Another example of the complexity of identity questions for living beings is the nature of the "self" in immunology. According to Carosella and Pradeu (2006) the classical model in immunology which rests upon the distinction between the self and the non self presupposes that every element external to the organism provokes a reaction designed to preserve its integrity. But immunitary reactions are not limited to exogenic factors (bacteries, parasites, foetuses are tolerated by the self).This is why, according to Carosella and Pradeu, the criterion of identity is continuity rather than identity. They show that any strong discontinuity within immune receptors and their targets gives rise to a reaction of the immune system, which does not discriminate between self and non-self, but between endogenous or exogenous epitopes which are constantly present and others which break the continuity of interactions. This is why, according to them, biological identity if nothing but a kind of continuity: "The continuity hypothesis conceives of identity as an identity-continuity, since it claims that nothing more than the spatiotemporal continuity of adhesions between immune receptors and ligands defines immune identity. This hypothesis can therefore be seen as the immunological point of view on the identity of organisms. According to the continuity hypothesis, nothing like a permanent 'core' to be preserved against all foreign threats is presupposed and thought to define immunity. Changes from the inside and changes from the outsideequally can trigger an immune response, depending on the conditions of encounter." (Pradeu and Carosella 2006: 247) Another problem raised by Wiggins' conception is that it seems to presupose a form of Aristotelian essentialism in biology. He holds in particular that the sortals upon which continuants depend are natural kinds. A number of writers, however, starting with David Hull, have held that biological entities such as species can be considered as individuals and not as kinds. If this is correct one would need a different conception of the the sortals upon which the continuants depend.

Most of the writers who criticize the use of the classical and absolute notion of identity suggest that we should dispense with these principles and replace them with principles for a weaker relation than identity, namely continuity, for which not all of the principles such as (Id ind) are valid. The view that identity principles can be in some sense reduced to the principles which hold for constitution (mostly distinct continuity principles for the various kinds of entities) raises, however, serious problems. The first one is that it resurrrects the ghost of the thesis of the relativity of identity, and of a pluralistic view according to which there are as many types of identity relations as there are principles of individuation in each domain. Thus there would be physical identity, biological identity, personal identity, social identity, etc. Some writers, like Boniolo and Carrara 2004, simply accept this form of relativism. But then it is hard to see how it can escape the difficulties adduced for Geach's view. Or one has simply to bite the bullet, and reject the classical and absolute notion of identity.

The second difficulty of the pluralistic or anti-essentialist conception consists in its reduction of identity to continuity. As many discussions on the problem of personal identity since Locke and Butler have shown, identity is not the same thing as continuity. 11

Functionalism about identity

How could we reconcile the unity and the absoluteness of the identity relation with the plurality of the modes of constitution and of the conditions of persistence of objets of different kinds? A possible solution takes its inspiration from the familiar functionalist conception of mental states in the philosophy of mind. According to functionalism, the mental properties of an organism are defined by the causal role of the properties of that organism. In most contemporary versions of the view, functional properties are secondorder properties: they are role-properties of first-order (physical and biological) properties of organisms. These roles are "multiply realised" in these first order properties of the organisms, and supervene upon them, without being identical to these properties. This functionalist picture can be extended to other kinds of abstract properties. In particular a number of writers have proposed that truth could be conceived as a functional property defined at the abstract level as satisfying a set of "platitudes", and realised in various domains [START_REF] Pettit | Realism and Truth, comments on Crispin Wright's Truth and Objectivity[END_REF][START_REF] Lynch | Alethic Functionalism and our Folk Theory of Truth[END_REF],2009). On Lynch's version of the view, Just as, according to functionalism about mental states, our use of "belief", "desire" and other mental terms can be individuated in terms of the role that they play, together with other states, in mediating between inputs and outputs, we could say that the predicate "true" is a place mark for a certain role marked by the usual platitudes: asserting statements that one believes, which correspond to reality, on which people can converge, etc. But the issue of the nature of the properties which "realise" these roles is left open.

Truth is a property which can be variably realized, just as a functional property can be so realised. Summarizing the idea, Wright says: « The concept of truth admits a uniform characterisation wherever it is appliedthe characterisation given by the minimal platitudes, which determine what is essential to truth…The form of pluralism for which space is allowed by this overarching uniformity is In other words truth is a second-order property, which has to be realised in various ways in first-order properties which will underlie this role. In each case we shall to give arguments to secure that the realist story is correct or not. The idea is close to one which had been advanced by David Wiggins in his theory of identity (Wiggins 1980). Identity is the one and only relation captured by the principles of reflexivity, symmetry, transitivity, substitutivity and the identity of indiscernibles, but there are varying conditions of identity for material objects, persons, events, biological beings, social objets , etc. Similarly truth is a multiply realizable role-property, which we can "ramsify" with a Ramsey sentence : X has a property that plays the truth role iff  t 1 ( t 1 … O 1 , …0 n ) & x has t n Cette conception fonctionnaliste de l'identité pose cependant problème si nous essayons de spécifier les rôles de la notion par rapport à ses réalisations dans différents domaines. Est-ce que l'on dira que l'identité est toute propriété qui joue le rôle d'identité, comme la continuité spatio-temporelle ou la similitude parfaite? Mais alors la notion d'identité se trouve à nouveau réduite à ces notions, ce qui est le contraire de ce qui était recherché. Dira-t-on que l'identité est la propriété du second d'ordre d'avoir la propriété qui joue le rôle de l'identité ? Mais quel serait ce rôle ? Une autre difficulté concerne la réalisabilité multiple, si nous poursuivons l'analogie avec le cas des propriétés mentales.

Selon la thèse de la réalisabilité multiple du fonctionnalisme du mental, il n'y a rien de The idea, as intimated, is that for each respect that is relevant in a context, the context contains a corresponding similarity space.13 If color is a relevant respect in C, then SC will contain a color space; if shape is relevant, SC will include a shape space; if time is relevant, it will include a temporal space; and so on. For each similarity space r 2 SC; let dr(_,_) be the distance function associated with that space; so dr(a,b) measures the distance between the representations of objects a and b in r. Also associated with each r 2 SC is a threshold value tr C >0; which may be different for different r and also-though for reasons given above this may be taken as optional-different for the same r in different contexts C. With this at hand, we can state a precise definition of folk identity: IdCða; bÞ () 8r 2 SC: drða; bÞ6tr C: ð1Þ

Variants of this definition are not hard to conceive. For example, we might stipulate that two objects are identicalC iff the sum of the distances between their various representations in the similarity spaces corresponding to the respects that are relevant in C does not exceed a certain threshold value, which depends on the context; or we might consider taking a weighted average of those distances, supposing that all relevant respects need not bear equally heavily on our identity judgments in a context. ??? Second, there is not the slightest linguistic evidence to suggest that the folk's identity judgments do not always respect the putative reflexivity and symmetry of the identity predicate. So presumably we should not regard as admissible explications of the phrase ''being highlyC similar in all relevantC respects'' that do not render folk identity reflexive and symmetric.

(1) entails a contextual version of Leibniz's Law. Within the similarity space approach, properties are representable as regions in the domain of a similarity space; for instance, the property blue corresponds to a certain region in color space

The analogy with functionalism, as we'll see shortly, is apt. But truth can't be a second-order property, for the reason just noted. That would imply that truth is the property of having some property that has certain features. But does the second-order property itself have those features? That is, it seems that we want to say that truth itself is objective and a goal of inquiry. But now is my belief's having the property of having a property that is a goal of inquiry a goal of inquiry? Well compare: suppose the color red is a second-order property: being red is having the property of having a property with certain features, such as a reflective variance. Does the property of having a property with a given reflective variance itself have that reflective variance? Not obviously; indeed, obviously not

  etc.) do not determine what kind of thing x and y are, or under what respect x and y are identical. In traditional terminology what determines which kind of thing is x is what individuates x, and individuation is another matter than identity.

  8 see Parfit 1984 : 205-206 . Wiggins dicusses these issues in chapter VII of Wiggins 2001 9 S. French et M. Redhead 1988 10 see in particular the intersting article by Boniolo and Carrara 2004

11

  See the classical objection to Locke by Joseph Butler, First Dissertation to the Analogy of Religion, 1736, rep in J. Perry, ed. Personal Identity, Berkeley University Press, Berkeley and Los Angeles, 1977 variable realisation. What constitutes the existence of a number is different from what constitutes the existence of a material object. » (Wright 1996)

  commun entre la propriété d'être une douleur dans un organisme et dans un autre. Mais alors comment peut-on parler d'identité ? La réponse est que, comme dans la conception fonctionnaliste du mentale, l'identité est une et plurielle. Il y a une et une seule propriété que toutes les entités d'un domaine particulier ont, l'identité. Elle se définit fonctionnellement par les propriétés formelles de la conception absolue de l'identité, c'est-à-dire (R,S, T, IndId et IndId). Mais elles la réalisent différemment. Pourtant les réalisations ne peuvent pas être parfaitement différentes d'un domaine à l'autre. Revenons au cas du soi immunitaire. Le fait que le soi ne soit pas une substance protégée de l'extérieur et qu'il n'y ait pas de « noyau » commun et permanent protégé contre des menaces extérieures implique-t-il qu'il n'y ait pas des lois causales qui définissent le système immunitaire? De nombreuses définitions de l'identité biologique : en font une forme d'intégration fonctionnelle. Un système est fonctionnellement intégré s'il régule fonctionnellement les activités pertinentes de ses parties sous un ensemble de conditions externes de manière à permettre l'autoreproduction et le maintien du système (autopoièse, homéostase). De même, si l'on prend un point de vue évolutionniste, on dira que chaque fonction est une fonction « propre » sélectionnée par le système dans son passé biologique. Je propose de considérer la propriété d'identité comme une telle propriété fonctionnelle, survenant sur les conditions variables d'individuation. Cette conception ne revient-elle pas à une forme d'essentialisme ? Oui, mais de l'essentialisme individuatif. Elle est en fait parfaitement comptatible avec celle de David Wiggins, et on peut la considérer comme un développement de cette dernière. La conception de David Wiggins et le fonctionnalisme quant à l'identité sont compatibles avec les faits propres à la continuité dans un domaine particulier, et l'identité peut demeurer ce qu'elle a toujours été, une propriété absolue, une affaire de tout ou rien.

A paradox, which, as Wiggins 2001 p.173-76 notes, comes from Chrysippus. The phrase comes from Peter Unger , see his 1980

cf.Wiggins, op.cit, ch.1, Engel 1989, op.cit, p. 241.

Oxford, Blackwell, 1980. The book had a first version in 1968, Identity and Spatio temporal continuity, and a third one as Sameness and Substance Renewed, Oxford University Press., 2001


Mlia Sadaf

Abdul Rauf

Franc ¸ois Yvon

LIMSI

This report describes LIMSI's submissions to the Round 1 of translation shared task at MLIA . We have submitted systems using various combinations of in-domain and out-of-domain corpora fine tuned on the MLIA COVID data, in order to develop resource-heavy systems for the translation of COVID mlia data from English into French, using two pre-processing pipelines and pretrained representations. Our experiments demonstrate the effectiveness of in-domain and task specific corpus, even if in small amounts.

Introduction

In Covid-19 MLIA @ Eval initiative, the Machine Translation (MT) task aims to organize a community evaluation effort for facilitating creation and dissemination of resources and tools for MT systems on Covid-19 related sentences. This domain falls under the category of biomedical domain, which is gaining interest owing to the unequivocal significance of medical scientific texts. The vast majority of these texts are published in English and Biomedical MT aims to also make them available in multiple languages. This is a rather challenging task, due to the scope of this domain, and the corresponding large and open vocabulary, including terms and non-lexical forms (for dates, biomedical entities, measures, etc). The quality of the resulting MT output thus varies depending on the amount of biomedical (in-domain) resources available for each target language.

We participated in round1 of MLIA translation task(3) for English to French direction. English-French is a reasonably resourced language pair with respect to Biomedical parallel corpora, allowing us to train our Neural Machine Translation (NMT) [START_REF] Sutskever | Sequence to sequence learning with neural networks[END_REF] with in-domain corpora as well as large out-of-domain data that exist for this language pair. Following [START_REF] Abdul-Rauf | LIMSI @ WMT 2020[END_REF], our main focus was to develop strong baselines by making the best of auxiliary resources. Two pre-prossessing pipelines, one using the standard Moses tools 1 and subword-nmt [START_REF] Sennrich | Neural machine translation of rare words with subword units[END_REF] and other using HuggingFace BERT API were developed. All systems are based on the transformer architecture [START_REF] Vaswani | Attention is all you need[END_REF], or and on the related BERTfused transformer model of Zhu et al. [START_REF] Zhu | Incorporating BERT into Neural Machine Translation[END_REF]. Our systems are presented in Section 3.1.

Translation from English into French

Data sources

We trained our baseline systems on a collection of biomedical corpora (in domain) and out-of-domain parallel corpus. We gathered indomain parallel corpora available for English-French in the biomedical domain. These included the biomedical texts provided by the WMT'20 organizers: Edp, Medline abstracts and titles [START_REF] Jimeno Yepes | Findings of the WMT 2017 biomedical translation shared task[END_REF], Scielo [START_REF] Neves | The Scielo Corpus: a parallel corpus of scientific publications for biomedicine[END_REF] and the Ufal Medical corpus2 consisting of Cesta, Ecdc, Emea (OpenSubtitles), PatTR Medical and OpenSubtitles. In addition, we used the Cochrane bilingual parallel corpus [START_REF] Ive | Diagnosing high-quality statistical machine translation using traces of post-edition operations[END_REF] 3 and the Taus Corona Crisis corpus. 4 . For out-of-domain corpus, we used the parallel corpora provided by the WMT14 campaign, which included Gigafr-en, Common crawl, Europarl, News Commentary and the UN corpora.

For development purposes, we used the tuning corpus provided by MLIA organisers and created a self-test corpus by selecting 1000 sentences randomly from the training corpus. The self-test corpus was not part of our mlia training corpus used to build the systems.

Pre and post-processing

The document level corpora were first retrieved from xml, split5 into sentences and sentence aligned using Microsoft bilingual aligner [START_REF] Moore | Fast and accurate sentence alignment of bilingual corpora[END_REF]: these include Cochrane, Scielo and some unaligned documents from Edp. All train, development and test corpora were cleaned by removing instances of empty lines, URLs and lines containing more than 60% non-alphabetic forms.

For tokenization into words and subwords units, two pipelines were considered. The first one is set up as follows (a) tokenize the French and English texts using Moses scripts6 ; (b) compute a joint Byte-pair Encoding (BPE) inventory of 32K units with subword-nmt;7 (c) generate the translation; (d) detokenize and truecase the output, again with Moses scripts. Systems based on this pipeline are prefixed M * . The second one is slightly more complex as it heavily relies on the HuggingFace API 8 for accessing pretrained BERT models. The corresponding systems are prefixed with H * or B * and comprise the following steps: (a) a simple tokenization script, (b) a multilingual segmenter mapping BPE units to pre-trained encodings generated according to [START_REF] Devlin | BERT: Pre-training of deep bidirectional transformers for language understanding[END_REF] as input to the translation system (step (c)). In that case, the MT output is also a sequence of multilingual BPE units that further needs (d) to be reaccentuated and recased, before a final (e) detokenization. Step (d) is non-trivial and is performed by a monolingual translation system trained to convert HuggingFace BPE units into Moses BPE units, 9 which can then be properly reassembled and detokenized as for the Moses pipeline.

3 Round 1

Translation Framework

All systems use Facebook's seq-2-seq library fairseq [START_REF] Ott | fairseq: A fast, extensible toolkit for sequence modeling[END_REF]. We mostly used two architectures to build our systems: basic and big Transformer models [START_REF] Vaswani | Attention is all you need[END_REF] as well as BERTfused transformer models [START_REF] Zhu | Incorporating BERT into Neural Machine Translation[END_REF]. For transformer small, the parameters settings are borrowed from transformer iwslt de en. 10 We used memory efficient FP16 optimizer. The ReLU activation function was used in all 6 encoder and 6 decoder layers, 1024 hidden layer size and batch size of 4K. Training was optimized using Adam and a learning rate of 0.0005 was fixed for all experiments. Systems based on transformer big borrowed settings from transformer vaswani wmt en fr big.

For the BERT-based models, we relied on BERT-NMT. 11 This allowed us to build the BERT-fused models using the same architecture and parameters as the baseline transformer models and to establish fair comparisons. In BERT-fused NMT model, the contextual representations are first computed by the BERT model for each token (in the source and target), these are then combined at each encoder and decoder layer using the attention mechanism. Full details are in Zhu et al. [START_REF] Zhu | Incorporating BERT into Neural Machine Translation[END_REF].

Given the large size of our training data in the unconstrained settings, the "lazy" output data set implementation was used to enable data loading in the RAM. Systems were trained until convergence based on the BLEU score on the development sets. Evaluation is performed using sacrebleu [START_REF] Post | A call for clarity in reporting BLEU scores[END_REF]. Scores are chosen based on the best score on the development set and the corresponding scores for that checkpoint are reported on the mlia self-test set and the scores provided by the organisers.

Constrained Systems

Constrained systems were built using only the training and development data provided by the MLIA organisers. BPE using 32K vocabulary units were learned only on the MLIA training and development corpus. The system submitted was built using transformer big, with settings being borrowed from transformer vaswani wmt en fr big.

It ranked third in evaluation with BLEU score of 43.5 and chrF score of 0.660 [START_REF] Casacuberta | The Covid-19 MLIA @ Eval initiative: Overview of the machine translation task[END_REF].

Unconstrained Systems

We experimented with several data combinations and frameworks and submitted four unconstrained systems. We will present the system in order of their rank according to round 1 evaluation scores. Our first unconstrained system M2 was built using all the in domain biomedical corpora listed in Table 1. The system was trained until convergence and then fine-tuned by continuing training on the MLIA data. As per the scores from evaluation campaign, this is the highest scoring system amongst the ones we submitted. M 3 and B4 are the systems that we built by first initialising the parameters from huge out-of-domain corpus and later fine tuning on in-domain corpus. The in-domain BPE codes learned from all the Biomedical data (other than mlia corpus) was used to segment the out-of-domain corpus. The initial systems were trained for 4 epochs on general domain WMT14 EN-FR corpora (see section 2.1 for corpus details). Model parameters were then freezed and used to initialize training for the in-domain system. The MLIA corpus was replicated two times to increase the probability distribution of COVID related sentences. M 3 uses the moses tokenisation pipeline whereas B4 is based on the hugging face pipeline as already detailed in Section 2.2. The two systems have the same BLEU score and a very close ChrF score as per MLIA campaign evaluation score. However, this is not the case for the scores on development data and the self-test data where B4 outperforms M 3.

The most interesting case is M 5, which is the system built using only MLIA corpus, but the bpe units are computed using the BPE codes of all the in-domain data. This can be called a semi-constrained system as the only difference from M 1 (the constrained system) is that for M 1, the bpe units were learned from MLIA corpus only, where as for M 5 bpe codes learned from all in-domain corpora are used. Despite being trained on a very small amount of corpus as compared to other unconstrained systems, the scores are almost comparable to the other systems as per MLIA evaluation results. Whereas, this system is the best scoring system as per mlia-self test data.

Our results show the importance of in-domain corpus. System trained on only small amount of MLIA corpus, with bpes learned from in domain corpora is very close to systems trained on huge general domain data and fine tuned on in domain corpora. The system built using only in-domain data was ranked third, while the rest four ranked forth in evaluation [START_REF] Casacuberta | The Covid-19 MLIA @ Eval initiative: Overview of the machine translation task[END_REF].

Conclusion

Our experiments for the first round show that training models on significantly fewer data (which has learned domain specific codes) results in better performance if the domain is very specific, COVID-19 related text in this case, and can be comparable to models that are trained on huge but less domain specific data.

Table 1 .

 1 Table 1 details the corpora used in training. Data sources for the English-French mlia task (before tokenization)

		Training
	Corpus	Words (M)	Sentences
		English	French
	In-domain	239379673 266842261	8139198
	Out-of-domain	1138581981 1292055231 35762532
	MLIA	19409220	22579335	1004174
	Mlia-dev	17006	18828	728
	Mlia-self	19704	22916	1000

Table 2 .

 2 Constrained and unconstrained systems submitted in round 1. M * prefixed systems were built using the moses tokenisation pipeline, while B * used HuggingFace pipeline.

	ID	Name Detail	Dev Self-test BLEU ChrF
			Constrained system
	M1	trans mlia	34.4	57.7	43.5 0.660
			Unconstrained systems
	M2	indom indom-ftmlia	36.8	56.5	51.2 0.721
	M3	trans outdom-ms-ftindom 33.8	45.5	49.3 0.710
	B4	bert	outdom-hg-ftindom 39.8	56.0	49.3 0.703
	M5	mlia	biobpe	36.4	58.5	48.5 0.705

https://ufal.mff.cuni.cz/ufal_medical_corpus

https://github.com/fyvo/CochraneTranslations/

https://md.taus.net/corona

https://github.com/berkmancenter/mediacloud-sentence-splitter

http://www.statmt.org/moses/

https://github.com/rsennrich/subword-nmt

https://Huggingface.co/transformers/model_doc/bert.html

This process is not completely error prone, and yields a BLEU score of 98.2 on Medline 18 test set.

https://fairseq.readthedocs.io/en/latest/models.html

https://github.com/bert-nmt/bert-nmt