Héber H Arcolezi
email: heber.hwangarcolezi@univ-fcomte.fr.

Selene Cerna

Jean-Franc ¸ois Couchot
email: jean-francois.couchot@univ-fcomte.fr.

Christophe Guyeux
email: christophe.guyeux@univ-fcomte.fr.

Abdallah Makhoul
email: abdallah.makhoul@univ-fcomte.fr.

Privacy-Preserving Prediction of Victim's Mortality and Their Need for Transportation to Health Facilities

Keywords: Emergency medical services, Decision support system, Privacy-preserving data mining, Machine learning, kanonymity, Differential privacy, Pre-hospital emergency care

Emergency medical services (EMS) provide crucial prehospital care, such as in the case of cardiac arrest, where the victim requires immediate first-aid. For this reason, it is vital to improving EMS response time. This paper proposes a novel methodology based on machine learning (ML) techniques to predict both the victims' mortality and their need for transportation to health facilities using data gathered from the start of the emergency call until the Departmental Fire and Rescue Service of the Doubs (SDIS25) is notified. We first analyzed SDIS25 calls to find out associations between the call processing times and victims' mortality, and to measure the variables' importance. Next, we validated our proposed MLbased methodology, where mortality could be predicted with accuracy and area under the receiver operating characteristic curve (AUC) scores of 96.44% and 96.04% respectively, while the need for transportation achieved an accuracy and AUC scores of 73.62% and 78.91%, respectively. What is more, we found out that it was still possible to predict both targets perturbating the input data by applying k-anonymity and differential privacy techniques. In conclusion, the results showed the potential of ML for EMS, which can be used as a decision-support tool to early identify mortality and the use of resources (transportation) and, thus, help EMS to save more lives and avoid service disruptions.

I. INTRODUCTION

A. Background

Emergency medical services (EMS) are a key component of healthcare systems around the world. An important measurement of their quality is their response time, which is measured from the time of the call to the time an ambulance arrives at the emergency scene. In fact, shorter ambulance response times are potential contributors to higher survival rates [START_REF] Chen | Demand forecast using data analytics for the preallocation of ambulances[END_REF], [START_REF] Byrne | Association between emergency medical service response time and motor vehicle crash mortality in the united states[END_REF] since every second is a matter of life. For instance, the response time also depends on how and by whom the call is processed in the EMS center [START_REF] Penn | When seconds count: A study of communication variables in the opening segment of emergency calls[END_REF]. For this reason, there is a need to optimize these services and take advantage of plenty of data gathered throughout the years in hospitals and EMS.

As reviewed in recent survey works [START_REF] Shafaf | Applications of machine learning approaches in emergency medicine; a review article[END_REF]- [START_REF] Stewart | Applications of machine learning to undifferentiated chest pain in the emergency department: A systematic review[END_REF], decisionsupport systems based on machine learning (ML) techniques have been proposed for application in emergency medicine. Indeed, in the context of this paper, for EMS, there are many interests in using ML methods for tasks such as: identifying possible medical conditions before arrival on emergency departments [START_REF] Kang | Artificial intelligence algorithm to predict the need for critical care in prehospital emergency medical services[END_REF], to predict ambulances' demand to allow their reallocation [START_REF] Chen | Demand forecast using data analytics for the preallocation of ambulances[END_REF], to predict ambulance response time [START_REF] Arcolezi | Preserving geo-indistinguishability of the emergency scene to predict ambulance response time[END_REF], [START_REF] Lian | Scalable real-time prediction and analysis of san francisco fire department response times[END_REF], to predict the ambulances' turnaround time in hospitals [START_REF] Cerna | Machine learning-based forecasting of firemen ambulances' turnaround time in hospitals, considering the COVID-19 impact[END_REF], to predict clinical outcomes [START_REF] Myoung Kwon | Deep-learning-based out-of-hospital cardiac arrest prognostic system to predict clinical outcomes[END_REF], to early identify clinical conditions on emergency calls [START_REF] Blomberg | Machine learning as a supportive tool to recognize cardiac arrest in emergency calls[END_REF], to recognize and predict service disruptions [START_REF] Cerna | Predicting fire brigades operational breakdowns: A real case study[END_REF], and so on.

In this paper, we analyze the case of the Departmental Fire and Rescue Service of the Doubs (SDIS25) in France, with data from 2015 until 2020. SDIS25 has 71 centers deployed in its territory and its service is activated through some emergency phone number (e.g., 18 or 112). Next, the call is treated by an operator, which collects the necessary information about the emergency (e.g., victims, location) and notifies the center(s) to deal with the intervention. Once the adapted armament is ready, the ambulance departs to the emergency scene and upon arrival, the crew provides first-aid treatment to the victim(s). After that, depending on the victim's status, the victim(s) is transported to some health facility (HF), e.g., hospital, private clinics, and so on. Lastly, the ambulance and its crew return to the SDIS25 center and are available again to attend other interventions.

Fig. 1 exemplifies the aforementioned workflow and the interval of interest we considered to predict whether the victim will die and if the ambulance will need to transport (or not) the victim to HFs. That is, we focus on the period comprising the time where the EMS call center's phone starts to ring until some center(s) is notified to handle the intervention or the call ends. Without loss of generality, 'Alert' can be either before or after the call ends. In this period, information about the call is recorded automatically together with the identity of the operator that treated the call. Besides, information about the intervention is manually recorded by the operator in a computerized system (e.g., location, observations). Lastly, the victim's information can be acquired during the call or not (e.g., unidentified victims in traffic accidents).

Accessible data

Delay to alert

Fig. 1: General workflow of SDIS25 when dealing with an emergency. We consider as "interval of interest" the time between the phone starts to ring until some center(s) is notified (i.e., 'Alerted') or the call ends. With all data accessible within this interval, the objectives are to predict victim's mortality and their need for transportation to health facilities.

B. Context of the problem

However, the collection of big data in real life, in particular medical data, leads to a major problem: the disclosure of personal and sensitive information [START_REF] Kaissis | End-to-end privacy preserving deep learning on multiinstitutional medical imaging[END_REF]. More precisely, in our problem, there are two entities we are concerned with, namely, call center operators and victims with regard to privacy. Indeed, data breaches are all too common [START_REF] Mccandless | World's biggest data breaches & hacks[END_REF], which endanger users' privacy and can lead to substantial losses for companies under the General Data Protection Regulation [START_REF]2018 reform of EU data protection rules[END_REF]. In addition, ML models trained with raw data can also indirectly reveal sensitive information. For instance, in [START_REF] Song | Machine learning models that remember too much[END_REF] the authors evaluate how some models can memorize sensitive information from the training data, and in [START_REF] Shokri | Membership inference attacks against machine learning models[END_REF], the authors investigate how ML models are susceptible to membership inference attacks. In the privacy-preserving data mining literature, there are few alternatives, e.g., objective perturbation [START_REF] Chaudhuri | Differentially private empirical risk minimization[END_REF], gradient perturbation [START_REF] Abadi | Deep learning with differential privacy[END_REF], and input data perturbation [START_REF] Kasiviswanathan | What can we learn privately?[END_REF]- [START_REF] Chamikara | Efficient data perturbation for privacy preserving and accurate data stream mining[END_REF], that can help to mitigate these problems. In this paper, we consider the latter input perturbation setting since it is independent of any ML algorithm in contrast with objective and gradient perturbations schemes and because others can utilize the sanitized data in other contexts (e.g., analysis).

In our case, with the raw dataset containing direct identifiers (e.g., names), one straightforward question as: "Is there any operator linked with an increased ratio of victims' death?" can be easily computed, which compromises the operators' privacy and can lead to social and/or economical damages. Similarly, one can easily access the reason for the intervention (e.g., cardiac arrest) and use this information to jeopardize the victims' privacy through discrimination in health insurance, for example. Besides, even by excluding direct identifiers, both victims' and operators' identities are still at risk of being retrieved. Indeed, attributes such as sex, age, and ZIP code (a.k.a. quasi-identifiers -QIDs) can be combined with public data to reidentify individuals [START_REF] Sweeney | k-anonymity: A model for protecting privacy[END_REF].

C. Motivations and contributions

From 2016 to 2020, the SDIS25 has presented an average increase of about 15% in the number of EMS calls (i.e., emergency interventions), comparing to 2015, reaching the highest peak in 2018 with an increase of 25%. And just as calls increased, the number of fatalities also increased, on average by 7%, with a peak of 17% in 2018. Similarly, the number of travels to HFs grew on average by 15%, with a peak in 2018 of 26%. This implies that the resources of SDIS25 were engaged for longer, so there were fewer resources in the centers. And with the present scarcity of resources in its service, the SDIS25 is vulnerable to a major crisis (e.g., pandemics, natural disasters), which puts the population at risk. For this reason, an intelligent system is needed to allow them to predict the urgency of the intervention (victim's mortality) and plan the distribution of resources that will be engaged (victim's transportation).

This way, within the interval of interest in Fig. 1 and with all the accessible information about the call processing time; operators' and victims' personal data, and the intervention itself, the purpose of this paper is to contribute with a novel ML-based methodology to predict both victims mortality and their need for transportation to HFs, which can be used as a decision-support system by SDIS25 (and EMS in general). Indeed, when a center has received the alert to go to an intervention, the system could launch its predictions and, thus, allow EMS to better determine their resources to provide faster response time (and possibly avoid victim's mortality) and to know that the engaged armament will be in use for less time (by not going to a hospital, for example). In addition, we take into consideration both victims' and operators' privacy and, hence, we developed and assessed the effectiveness of two state-of-the-art privacy notions on sanitizing the datasets before training ML models. In summary, this paper makes the following contributions: I Variables' impact. Extract mortality and transportation statistics from victims, discover and address privacy issues, and finally recognize the variables with the greatest impact for building predictive models. This would allow replication of the process in another EMS. II Prediction of victims' mortality: Predict if the victim will die. This would allow to increase the level of urgency of the call and to improve the selection of adapted engaged resources. III Prediction of victims' transportation: Predict the need to transport the victim from emergency scenes to HFs. This would allow knowing if the EMS resources will be engaged for a longer period of time, and as a result, to make a better decision to deploy its resources. IV Privacy-conscientious predictions: In both items II and III, we take into consideration both victims' and operators' privacy. Indeed, we consider the privacy-preserving data mining setting named input data perturbation [START_REF] Kasiviswanathan | What can we learn privately?[END_REF]- [START_REF] Chamikara | Efficient data perturbation for privacy preserving and accurate data stream mining[END_REF]. This allows EMS to sanitize the data before transmitting it to third parties in charge to build ML-based decision-support systems.

Paper's outline: The remainder of this paper is organized as follows. In Section II, we describe the material and methods used in this work, i.e., the collected data and its analysis; the ML techniques, the privacy models, and the proposed methodology. In Section III, we present the results of our experiments and in Section IV our discussion with related work. Lastly, Section V shows our concluding remarks.

II. MATERIAL AND METHODS

A. Data collection

We used retrospective data recorded by SDIS25 from January 2015 to December 2020. All calls made to SDIS25 lines (e.g., 18 and 112) were considered. Calls that had an intervention identifier indicating that they were attended by SDIS25 centers were eligible for inclusion in the case there were victims. In total, after removing outlying observations, the primary dataset at our disposal comprises 177883 emergency calls with the following explanatory variables:

• Victim: age, sex, and center that assisted the victim; the city where the intervention occurred; distance between the center and the city; victim's mortality and victim's transportation to HFs. • Operator: age, sex, grade, and seniority (experience time).

• Call/Intervention: hour, day, day of the week, month, year, delay time to answer the phone, call duration, delay time to diffuse the alert, and type of intervention. The latter is described by 3 variables: type of operation (aid to person, fire, etc), subtype of operation (an emergency, fire on the public road, fire in an individual room, etc), and the motive for departure (external hemorrhage, respiratory distress, etc). We also have the reason for departure. The difference between the motive and reason is that the first is what is recorded by the operator based on the call received (partial), and the second is what is recorded by the firefighters upon return from the mission (confirmed). This last one will not be considered during the modeling since the developed system will make predictions before the armament departs to the mission. From here, we extracted 2 variables as our predictive targets: the victim's mortality and the need for transport to a hospital. Both will be developed in the following sections.

B. Data analysis and privacy awareness

Table I exhibits for each year the number (Nb.) of EMS calls, mortality, and transportation to HFs, and the augmentation (Growth in %) throughout years in comparison with 2015. The last row named 'Total' indicates the sum for Nb. and the average for Growth. One can notice that the total number of mortality and transportation to HFs represent 1.94% and 78.72% of the total number of EMS calls, respectively. Also, over the years, the number of EMS calls increased by 14.67% on average, which led to an average increase of 7.17% and 15.27% on the number of fatalities and transportation to HFs, respectively.

Fig. 2 presents statistics on call processing times by time intervals in seconds and their ratio of deaths as a percentage. One can observe that the ratio of deaths increases in the 3 time periods as time increases. This is more noticeable with 'Call duration' that reaches a rate of 28.57% of deaths when the calls lasted between 17 and 18 minutes (interval 1020-1080). Although, there were few calls [START_REF] Kaissis | End-to-end privacy preserving deep learning on multiinstitutional medical imaging[END_REF], more cases of deaths according to call center operators' delay time to answer the phone, the total call duration time, and the delay time taken to broadcast the alert, respectively, by time intervals in seconds. appeared ( 4). Yet, we still kept these cases since they could influence the prediction of victim's mortality.

Furthermore, on analyzing the attributes motive and reason for departure, we remark that about 75% of the times both values were equal. This means, most of the time, the information was correctly acquired during the call, which helps SDIS25 to correctly define the armament needed to attend the victim, and could contribute to the accuracy of our ML models launched before the departure of the armament.

With regard to privacy, considering victims, by combining three available QIDs (sex, age, and city), one can find about 22000 cases with the trivial k = 1-anonymity level [START_REF] Sweeney | k-anonymity: A model for protecting privacy[END_REF] (further explained in Subsection II-D). This means, in some cities with low population density, it would not be difficult to find out the person who needed help by knowing their sex and age. Similarly, combining four QIDs considering operators (sex, age, grade/career, and seniority) leads to a similar output with many unique rows. One exception is that there is a set of operators, and each row represents an event of who treated the emergency call. This reinforces the need for applying privacypreserving techniques to protect the users' privacy.

C. Machine learning techniques

Given the easy and fast use of techniques based on decision trees with tabular data, we selected 2 remarkable representatives: Light Gradient Boosted Machine (LGBM) and Extreme Gradient Boosting (XGBoost). Also, given the large amount of data we have and the recognized potential of neural networks, we tested 2 types: Convolutional Neural Network (CNN) and Attentive Interpretable Tabular Learning (TabNET). These 4 techniques are described briefly in the following:

• LGBM [START_REF] Ke | Lightgbm: A highly efficient gradient boosting decision tree[END_REF] is a gradient boosting decision tree technique. It establishes a leaf-wise tree growth strategy to speed up computation and reduce memory consumption.

• XGBoost [START_REF] Chen | XGBoost: A Scalable Tree Boosting System[END_REF] is a robust gradient boosting decision tree technique and a pioneer in optimizing tree parallelization. Its main strategy is adding penalization to the model's complexity to avoid overfitting.

• CNN [START_REF] Goodfellow | Deep learning[END_REF] is a type of deep neural network, applied mainly in the recognition and classification of images, but also texts and tabular data. Its 2 main layers are Conv and MaxPooling, where the first maps patterns and the second reduces the dimensionality of the drawn map.

• TabNET [START_REF] Arik | Tabnet: Attentive interpretable tabular learning[END_REF] is an interpretable canonical deep learning architecture for tabular data. It uses instance-wise feature selection strategy (attentive transformer) to improve nonlinear processing without falling into overfitting.

D. Privacy models

In this work, we applied and compared two state-of-theart privacy models to sanitize our datasets, which are briefly described in the following:

• K-anonymity (K-Anon) [START_REF] Sweeney | k-anonymity: A model for protecting privacy[END_REF]: The K-Anon model requires that each released record to be indistinguishable from at least k -1 others. Intuitively, the larger k is, the better the privacy protection will be. On applying K-Anon, there is a difference between explicit identifiers (e.g., names), which are removed or masked to avoid direct re-identification; sensitive attributes (e.g., mortality), that might be preserved, and quasi-identifiers (e.g., age, sex), in which K-Anon seeks to ensure indistinguishability. We recall the definition of K-Anon in the following. Definition 1 (k-anonymity requirement [START_REF] Sweeney | k-anonymity: A model for protecting privacy[END_REF]): Each release of data must ensure that every combination of values of QIDs can be indistinctly matched to at least k individuals. • Differential privacy (DP) [START_REF] Dwork | Calibrating noise to sensitivity in private data analysis[END_REF], [START_REF] Dwork | The algorithmic foundations of differential privacy[END_REF]: DP, originally proposed in [START_REF] Dwork | Calibrating noise to sensitivity in private data analysis[END_REF], is the current standard for data privacy. A formal definition of DP is given in the following: Definition 2 (( , δ)-Differential Privacy [START_REF] Dwork | The algorithmic foundations of differential privacy[END_REF]): Given > 0 and 0 ≤ δ < 1, a randomized algorithm A is said to provide ( , δ)-differential-privacy if, for all neighbouring datasets D 1 and D 2 that differ on the data of one user, and for all sets R of outputs:

Pr[A(D 1 ) ∈ R] ≤ e Pr[A(D 2 ) ∈ R] + δ.
The additive δ on the right-side of Eq. ( 2) is interpreted as a probability of failure. Normally, a common choice for δ is to set it significantly smaller than 1/n where n is the number of users in the database [START_REF] Dwork | The algorithmic foundations of differential privacy[END_REF].

E. Proposed ML-based methodology

This article proposes a new methodology based on ML techniques to predict the mortality of a victim and their need to be transported or not to an HF.

From our primary dataset, we modified the name of the victim's city (VIC CITY) by a numerical identifier generated based on the proximity between cities, i.e., we took as references the centroid of the 3 main cities of the region, we calculated the distances with the centroid of the other 570 cities in the territory, and we assigned the identifiers in ascending order of distance. This way, it is easier to define the generalization of hierarchies (by masking) during sanitization.

To increase the impact of the predictors, we added 6 other variables by combining the existing ones. The first 2 were:

• Age group (AGG GROUP AGE). The age of the victims was grouped into 8 categories. This variable was only used in the original dataset since sanitized datasets already group age in order to respect K-Anon (cf. Table III). • Time between rings the phone until the alert is broadcast (AGG INT TM TOTAL). It is the sum of delay time to answer the phone, call duration, and delay time to diffuse the alert.

Then we sort our dataset in ascending order by datetime and divide it into a training set (calls from 2015-2019) to build our models and testing set (calls from 2020) to validate the performance of the models. Finally, we add 4 more predictors:

• Probability of mortality by motive (AGG MORT PROBA MOT). We took the training set and grouped the calls in which the victims died by intervention type (type, subtype, and motive of departure). The number of cases by intervention type is divided by the total number of deaths. This results in a probability, where the probabilities > 0 are stored in a temporary table. The testing set samples are completed by looking for their probability in the temporary table. If the intervention's type is not found, the sample will receive a probability of zero, and the table will be updated for the next sample. Otherwise, the sample would take the current probability, and again the table would be updated. This follows the actual process, where the death of the victim is confirmed only when the firefighters return from their mission. It follows the same process of AGG MORT PROBA AGE, but with the "non-transportation to HFs" target. The categorical variables such as: the grade and sex of the operator, the sex and city of the victim, the center that attended the victim, the intervention's type, the weekday and the month were converted using the LabelEnconder method of Scikit-Learn, and the remaining variables that are numerical maintained their original scale.

Fig. 3 presents the interaction of our 2 final models developed in 2 stages as explained in the following: Stage 1: Prediction of victims' mortality. In this stage, the objective is to predict whether or not the victim is at great risk of dying if they are not treated quickly. This is represented by the binary target variable VICTIM MORTALITY (0: alive, 1: dead). The used dataset is composed of all the explanatory variables of the primary dataset together with the modified ones and the new ones (AGG GROUP AGE, AGG INT TM TOTAL, AGG MORT PROBA MOT, AGG MORT PROBA AGE). Since there is an imbalance in the number of samples between classes 0 and 1 (see Subsection II-B), we sought to compensate for the balance by using the Adaptive Synthetic sampling approach (ADASYN) and sample duplication, both only in the training set. In our preliminary experiments, duplication of samples in class 1 presented better results than ADASYN and, thus, duplication was used to construct the final models.

The specifications for the training process by technique is described in the following:

• LGBM: objective="binary", is unbalance=True, importance type="gain", boosting type="gbdt", and the search space was n estimators [50-1000], learning rate [0.001-0.8], max depth [START_REF] Chen | Demand forecast using data analytics for the preallocation of ambulances[END_REF][START_REF] Byrne | Association between emergency medical service response time and motor vehicle crash mortality in the united states[END_REF][START_REF] Penn | When seconds count: A study of communication variables in the opening segment of emergency calls[END_REF][START_REF] Shafaf | Applications of machine learning approaches in emergency medicine; a review article[END_REF][START_REF] Tang | Artificial intelligence and machine learning in emergency medicine[END_REF][START_REF] Stewart | Applications of machine learning to undifferentiated chest pain in the emergency department: A systematic review[END_REF][START_REF] Kang | Artificial intelligence algorithm to predict the need for critical care in prehospital emergency medical services[END_REF][START_REF] Arcolezi | Preserving geo-indistinguishability of the emergency scene to predict ambulance response time[END_REF][START_REF] Lian | Scalable real-time prediction and analysis of san francisco fire department response times[END_REF][START_REF] Cerna | Machine learning-based forecasting of firemen ambulances' turnaround time in hospitals, considering the COVID-19 impact[END_REF], and colsample by tree [0.5-1]. • XGBoost: objective="binary:logistic", boosting type="gbtree", and the tunned hyperparameters were n estimators [50-1000], learning rate [0.001-0.5], max depth [START_REF] Chen | Demand forecast using data analytics for the preallocation of ambulances[END_REF][START_REF] Byrne | Association between emergency medical service response time and motor vehicle crash mortality in the united states[END_REF][START_REF] Penn | When seconds count: A study of communication variables in the opening segment of emergency calls[END_REF][START_REF] Shafaf | Applications of machine learning approaches in emergency medicine; a review article[END_REF][START_REF] Tang | Artificial intelligence and machine learning in emergency medicine[END_REF][START_REF] Stewart | Applications of machine learning to undifferentiated chest pain in the emergency department: A systematic review[END_REF][START_REF] Kang | Artificial intelligence algorithm to predict the need for critical care in prehospital emergency medical services[END_REF][START_REF] Arcolezi | Preserving geo-indistinguishability of the emergency scene to predict ambulance response time[END_REF][START_REF] Lian | Scalable real-time prediction and analysis of san francisco fire department response times[END_REF][START_REF] Cerna | Machine learning-based forecasting of firemen ambulances' turnaround time in hospitals, considering the COVID-19 impact[END_REF][START_REF] Myoung Kwon | Deep-learning-based out-of-hospital cardiac arrest prognostic system to predict clinical outcomes[END_REF][START_REF] Blomberg | Machine learning as a supportive tool to recognize cardiac arrest in emergency calls[END_REF][START_REF] Cerna | Predicting fire brigades operational breakdowns: A real case study[END_REF][START_REF] Kaissis | End-to-end privacy preserving deep learning on multiinstitutional medical imaging[END_REF][START_REF] Mccandless | World's biggest data breaches & hacks[END_REF][START_REF]2018 reform of EU data protection rules[END_REF][START_REF] Song | Machine learning models that remember too much[END_REF][START_REF] Shokri | Membership inference attacks against machine learning models[END_REF][START_REF] Chaudhuri | Differentially private empirical risk minimization[END_REF][START_REF] Abadi | Deep learning with differential privacy[END_REF], colsample by tree [0.2-1], and scale pos weight .

• CNN: we extracted 10% of the training samples for the validation set. In addition, 4 types of architectures were built using Keras library, their structure are presented in Table II. The main hyperparameters were loss="BinaryCrossentropy", optimizer=Adam, epochs=1000, monitor="val loss", mode="min", pa-tience=15, restore best weights=True. And the tunned hyperparameters were batch size , learning rate [0.0001-0.2], and the architecture's type [START_REF] Chen | Demand forecast using data analytics for the preallocation of ambulances[END_REF][START_REF] Byrne | Association between emergency medical service response time and motor vehicle crash mortality in the united states[END_REF][START_REF] Penn | When seconds count: A study of communication variables in the opening segment of emergency calls[END_REF][START_REF] Shafaf | Applications of machine learning approaches in emergency medicine; a review article[END_REF]. n shared [START_REF] Chen | Demand forecast using data analytics for the preallocation of ambulances[END_REF][START_REF] Byrne | Association between emergency medical service response time and motor vehicle crash mortality in the united states[END_REF][START_REF] Penn | When seconds count: A study of communication variables in the opening segment of emergency calls[END_REF][START_REF] Shafaf | Applications of machine learning approaches in emergency medicine; a review article[END_REF][START_REF] Tang | Artificial intelligence and machine learning in emergency medicine[END_REF], gamma [START_REF] Chen | Demand forecast using data analytics for the preallocation of ambulances[END_REF][START_REF] Byrne | Association between emergency medical service response time and motor vehicle crash mortality in the united states[END_REF], lr [0.001-0.5], and batch size .

Finally, to search hyperparameters for each technique, we used Bayesian optimization through the Hyperopt library with the Tree Parzen Estimator Suggest (tpe.suggest) and 500 iterations. The objective function employed to select the best victim mortality model (VM model) is a combination of Accuracy (ACC), Balanced Accuracy (BACC), Macro F1 score (MF1), and Recall of class 1 in the form of maximize(ACC 2 ×Recall 2 × BACC × M F 1). This is because we wanted to keep the models with high ACC and Recall without losing the balance between classes due to the class imbalance problem. Stage 2: Prediction of victims' transportation. This stage predicts whether the victim will need or not to be transported to an HF. The target is represented by a binary variable VICTIM TRANSPORTATION (0: needed, 1: did not need). Given that most cases require (see Subsection II-B) a transfer to an HF (0), it would be more hard but advantageous to detect those calls that need the resources for less time (1), thus, recognize that the armament will return faster to the center and there will be more resources available ready to attend other interventions. The dataset used in this stage included as an explanatory variable the predicted victim mortality since if the prediction indicates a death, there will be a greater probability of going to an HF to save the victim's life. Therefore, the engaged armament will be unavailable for a longer time. Other predictors considered are all those defined in stage 1, and AGG TRAN PROBA MOT and AGG TRAN PROBA AGE. Unlike the previous phase, no duplication or generation of artificial samples was applied since no improvement was observed in the preliminary tests. Finally, we used the same search space and model selection process applied in stage 1 to choose the best victim transportation model (VT Model). Experiments with sanitized data. In the context of this paper (i.e., of medical data), we used the differentially private data release mechanism proposed in [START_REF] Bild | SafePub: A truthful data anonymization algorithm with strong privacy guarantees[END_REF], which produces truthful data output. More precisely, DP is ensured by sub-sampling, in which the sampling probability depends on , and data are released in a generalized form that also satisfies K-Anon (where k depends on and δ). In our experiments, we set = 1, which is a common value in DP literature [START_REF] Dwork | The algorithmic foundations of differential privacy[END_REF], [START_REF] Bild | SafePub: A truthful data anonymization algorithm with strong privacy guarantees[END_REF] and we set δ = 10 -6 1/n. With these parameters, the differentially private training set was sub-sampled from 149321 to 81538 samples and, besides DP guarantees, K-Anon is also satisfied with k = 74 [START_REF] Bild | SafePub: A truthful data anonymization algorithm with strong privacy guarantees[END_REF]. Thus, for a fair comparison between the two privacy models, we also set k = 74 when applying the K-Anon model individually. In other words, we can thus evaluate the impact of having only a K-Anon guarantee in comparison with the case of DP that also satisfies K-Anon guarantees.

Table III exhibits the final generalization approach for each QID we considered of each entity (Victim -Vic. and Operator -Ope.) and privacy model (K-Anon and DP). The symbol * in Table III indicates full suppression for an attribute or masking of a digit (for Vic. City). Also, we highlight that both privacy models were applied only in the training set and, hence, the testing set was transformed using the final generalization hierarchies.

Finally, with the sanitized datasets, we selected only the ML technique that performed the best with original data among the four we evaluated (i.e., LGBM, XGBoost, TabNET, and CNN). Similar to the 2-stage methodology previously explained, we used Bayesian optimization with 500 iterations for the first VM Model, and its predictions were also used as input to the subsequent VT Model for 500 iterations too. Lastly, models were evaluated with the aforementioned classification metrics.

III. RESULTS

Table IV exhibits for each dataset (original and sanitized ones) the metrics results considering each experimented ML technique calculated for each target and all samples from 2020. We also included the metrics: Area Under the Receiver Operating Characteristic Curve (AUC) and the Precision of class 1. From Table IV, one can notice that for ML models trained with original data, XGBoost consistently outperformed all the other models in both binary classification tasks, with results highlighted in bold. This is why for sanitized datasets, we only present results with XGBoost.

In general, one can notice that the developed models reached high scores when predicting victims' mortality, with ACC, BACC, and AUC scores higher than 88% getting to 96%. Also, as an imbalanced classification problem, for mortality, all models achieved M-F1 scores of about 70% ∼ 75% since they had lower precision scores 30% ∼ 36% for the minority class (victim will die -1) while achieving a good recall of about 80% ∼ 85%. On the other hand, the results for classifying if the ambulance will return to the EMS center (positive class -1) or will transport the victim to HFs (negative class -0) were not as good as for the victims' mortality target. In this case, all models achieved intermediate scores of about 70% ∼ 78% for ACC, BACC, and AUC. Besides, the M-F1 metric decreased to about 65% ∼ 68% with lower recall values ranging from 66% ∼ 71% and higher precision scores 40% ∼ 44% in comparison with predicting mortality.

Moreover, one can notice some minor decrease in the performance scores when comparing the XGBoost model trained with original and sanitized datasets. Indeed, although some features (the QIDs) suffered transformation and/or suppression, models were still able to classify both targets as good as with the original dataset, while providing privacy guarantees for both victims and operators. These results suggest that some patterns were kept even with the transformed features. To analyze this behavior, Fig. 4 illustrates the Pearson correlation coefficient ranging from -1 (negative correlation) to +1 (positive correlation), considering all the variables of the 3 types of dataset. We highlight that in the case of sanitized datasets we transformed the variable names used as QIDs following the acronym 'K' and 'DP' (e.g., K OPE AGE). One can notice that in the 3 datasets, few of the initial variables have a slight impact (VIC However, by combining some of these (see Subsection II-E) and generating the aggregates (AGG prefix) we obtain variables with more correlation (AGG MORT PROBA AGE, AGG MORT PROBA MOT, AGG TRAN PROBA AGE, and AGG TRAN PROBA MOT) even with sanitization.

In addition, Fig. 5 illustrates the 12 features with the highest impact by target, dataset, and best prediction model generated by the XGBoost "Gain" feature importance algorithm. This is based on the relative contribution of each feature to improve the accuracy in the division of a branch. Thus, from Fig. 5, we can confirm that the aggregate variables generated from probabilities and the type of intervention (type, subtype, and motive) have a great impact on the creation of both models. In the case of victim's mortality, age and sex are more important than the alert diffusion time and duration of the call. In addition to that, we discovered that the time and day of the week also have an impact on the model. In the case of nontransportation of the victim to an HF, the greatest impact is generated by the mortality of the victim and, to a lesser degree, the sex, the hour of the call, and the center from which the ambulance departed. Although the age of the victim did not show influence when it was sanitized, it did show an effect with the original data. Moreover, in our case, operators' personal data did not show much importance for any ML model, in this way, for upcoming works, we consider not using such predictors as there would be a need for preserving their privacy. We believe that our analysis of feature importance can provide an overall idea of what other EMS and research groups might consider with the intention of replicating this work.

IV. DISCUSSION AND RELATED WORK

When reviewing the related works, we find that some EMS are exploiting their data with ML techniques [START_REF] Chen | Demand forecast using data analytics for the preallocation of ambulances[END_REF], [START_REF] Shafaf | Applications of machine learning approaches in emergency medicine; a review article[END_REF]- [START_REF] Lian | Scalable real-time prediction and analysis of san francisco fire department response times[END_REF], tion to health facilities (HFs) using data available at the start of the emergency call until an EMS center is notified. The results indicate that mortality could be predicted with both accuracy and AUC scores as high as 96%. On the other hand, the need for transportation to HFs could be predicted with intermediate accuracy and AUC scores of about 70% ∼ 78%. These results showed the potential of ML for EMS, which can be used as a decision-support tool to early identify mortality and the use of resources (transportation) and, thus, help EMS to save more lives and avoid service disruptions. In addition, we also took into consideration both victims' and call center operators' privacy when training ML models. In this case, even with sanitized datasets (k-anonymous and differentially private), it was still possible to predict the intended targets. With these findings, EMS may consider using and/or sharing privatized datasets to avoid possible data leakages, membership inference attacks, and data reconstruction attacks [START_REF] Mccandless | World's biggest data breaches & hacks[END_REF], [START_REF] Song | Machine learning models that remember too much[END_REF], [START_REF] Shokri | Membership inference attacks against machine learning models[END_REF]. Lastly, some limitations and prospective directions of this paper are described in the following. First, on sanitizing the datasets, there is a clear difference in the type of privacy we provided for each entity. On the one hand, because victims were unique in our dataset, DP and K-Anon provided userlevel [START_REF] Dwork | The algorithmic foundations of differential privacy[END_REF] privacy. On the other hand, there is a unique set of operators that treated many emergency calls and, thus, DP and K-Anon provided event-level [START_REF] Dwork | The algorithmic foundations of differential privacy[END_REF] privacy. Investigating a uniform notion of privacy for both entities is an intended direction. Also, we considered an ideal case where the information of all victims in the testing set was acquired during the call. However, this may not always occur in real life, e.g., when someone activates EMS for unidentified victims. One future direction would be evaluating our models with randomly excluded data from victims (i.e., sex and age) to assess the ML models' robustness. Other future directions would be working with the observations registered by operators during calls in text format, which could be treated with natural language processing techniques, as well as voice registers.

Fig. 2 :

 2 Fig.2: Ratio of victims' death (Nb. Deaths/N b. Calls × 100) according to call center operators' delay time to answer the phone, the total call duration time, and the delay time taken to broadcast the alert, respectively, by time intervals in seconds.

Fig. 3 :

 3 Fig. 3: Proposed ML-based methodology developed in 2 stages. Stage 1 predicts the victim's mortality, which will be used as a feature in stage 2 when predicting the need to transport the victim to an HF.

  • TabNET: we extracted 10% of the training test to be used as a validation set during the training process. The main specifications were optimizer="Adam", eval metric="logloss", max epochs=1000, and patience=15. The hyperparameters tunned were n d[START_REF] Penn | When seconds count: A study of communication variables in the opening segment of emergency calls[END_REF][START_REF] Shafaf | Applications of machine learning approaches in emergency medicine; a review article[END_REF][START_REF] Tang | Artificial intelligence and machine learning in emergency medicine[END_REF][START_REF] Stewart | Applications of machine learning to undifferentiated chest pain in the emergency department: A systematic review[END_REF][START_REF] Kang | Artificial intelligence algorithm to predict the need for critical care in prehospital emergency medical services[END_REF][START_REF] Arcolezi | Preserving geo-indistinguishability of the emergency scene to predict ambulance response time[END_REF][START_REF] Lian | Scalable real-time prediction and analysis of san francisco fire department response times[END_REF][START_REF] Cerna | Machine learning-based forecasting of firemen ambulances' turnaround time in hospitals, considering the COVID-19 impact[END_REF], n a [1-10], n steps [2-10], n independent [1-5],

TABLE I :

 I Summary statistics on the number (Nb.) of EMS calls, mortality, and transportation to HFs and the augmentation (Growth) in relation to the baseline year 2015. Total indicates the sum for Nb. and the average for Growth.

	Year	Nb.	EMS Calls Growth (%)	Nb.	Mortality Growth (%)	Nb.	Transport Growth (%)
	2015	26417	-	544	-	20700	-
	2016	28529	7.99	532	-2.21	22479	8.59
	2017	31311	18.53	562	3.31	24990	20.72
	2018	33150	25.49	638	17.28	26271	26.91
	2019	29914	13.24	562	3.31	23370	12.90
	2020	28562	8.12	621	14.15	22214	7.31
	Total	177883	14.67	3459	7.17

  AGG TRAN PROBA MOT). Its process is similar to the variable AGG MORT PROBA MOT, with the difference that we exchanged deaths for non-transportation to HFs.• Probability of transport by age (AGG TRAN PROBA AGE).

	• Transport	probability	by	motive
	(

• Probability of mortality by age (AGG MORT PROBA AGE).

The training set data that resulted in deaths are grouped by motive of departure and AGG GROUP AGE. In this way, the number of cases per category is divided between the total deaths to generate a probability and create a temporary table with the values > 0. The assignment of probabilities to the testing set follows the same process of the variable described previously.

TABLE II :

 II Defined architectures for CNN with the number of neurons (nn), pool size (s), and dropout rate (r) used.

	Archi. 1	Archi. 2	Archi. 3	Archi. 4
	Input	Input	Input	Input
	BatchNormalization BatchNormalization BatchNormalization BatchNormalization
	Conv1D (nn=128)	Conv1D (nn=512)	Conv1D (nn=32)	Conv1D (nn=32)
	MaxPooling1D (s=2) MaxPooling1D (s=2) MaxPooling (s=2) MaxPooling (s=2)
	Flatten	Flatten	Dropout (r=0.2)	Dropout (r=0.2)
	Dense (nn=2)	Dense (nn=2)	Conv1D (nn=64)	Conv1D (nn=64)
	Activation (sigmoid) Activation (sigmoid) MaxPooling (s=2) MaxPooling (s=2)
			Flatten	Dropout (r=0.5)
			Dense (nn=2)	Conv1D (nn=128)
			Activation (sigmoid) MaxPooling (s=2)
				Flatten
				Dense (nn=2)
				Activation (sigmoid)

TABLE III :

 III Final generalization hierarchy for each QID of each entity, namely, victim and call center operator.

	Attribute	Final Generalization Hierarchy
		k-Anonymity	Differential Privacy
	Vic. Age	[0, 64[, [64, 101[	[0, 32[, ..., [96, 101[
	Vic. Sex	M, F, NR	M, F, NR (not registered)
	Vic. City	21***, 22***, 23***	212**, 222**, ..
	Ope. Age	[22, 38[, ..., [54, 63[, ≥63	[22, 30[, [30, 38[, ... ≥62
	Ope. Sex	F, M	F, M
	Ope. Seniority [0, 5760[, [5760, 10204[, ≥10204	*
	Ope. Grade	*	*

  SEX/K VIC SEX/DP VIC SEX,

			INT OPERATION TYPE,
	INT OPERATION SUBTYPE,	and	INT MOTIVE DEPARTURE).

TABLE IV :

 IV Results of the best models by ML technique with and without privacy-preserving sanitization for 2020.

	Dataset ML Technique	Victim's Mortality (%) ACC BACC AUC MF1 Recall Precision ACC BACC AUC MF1 Recall Precision Victim's Transportation (%)
		LGBM	96.07 90.83 95.60 73	85	34	73.53 70.99 73.78 67	66	44
	Original	XGBoost CNN	96.44 90.86 96.04 75 95.97 89.44 94.63 73	85 83	36 33	73.62 72.63 78.91 68 70.42 70.30 75.76 65	71 70	44 40
		TabNET	95.39 90.24 94.97 71	85	30	70.98 70.26 74.17 65	69	41
	K-Anon	XGBoost	96.26 91.00 95.50 74	86	35	73.62 72.52 78.70 68	71	44
	DP	XGBoost	96.04 90.18 95.89 73	84	34	73.22 72.35 78.53 68	71	44

* These are co-first authors that contributed equally to this work. This work was supported by the EIPHI-BFC Graduate School (contract "ANR-17-EURE-0002"), by the Region of Bourgogne Franche-Comté CAD-RAN Project, and by SDIS du Doubs, with the support of the French Ministry of Higher Education and Research (managed by the National Association of Research and Technology (ANRT) for the CIFRE thesis (N 2019/0372). The authors would also like to thank SDIS 25 Commander Guillaume Royer-Fey and Captain Céline Chevallier for their great collaborations and continuous feedback. All computations have been performed on the "Mésocentre de Calcul de Franche-Comté".

[11]- [START_REF] Cerna | Predicting fire brigades operational breakdowns: A real case study[END_REF]. For instance, in [START_REF] Chen | Demand forecast using data analytics for the preallocation of ambulances[END_REF], the authors identified that shorter response time is associated with a higher survival rate and predicted the demand of ambulances to allow their reallocation. In [START_REF] Blomberg | Machine learning as a supportive tool to recognize cardiac arrest in emergency calls[END_REF], the authors used an ML framework to early recognize cardiac arrest by voice records in emergency calls. The latter consider an interval of interest similar to ours (Fig. 1), with the difference that we use tabular data recorded in the last 5 years, and where our first objective is to predict the victim's mortality. Since this prediction is done before dispatching ambulances, EMS could activate proactive decisions to mobilize their armament and provide quicker response times. In addition, we also propose to use the prediction of the victim's mortality as an input to a second model (cf. Fig. 3), which predicts if the ambulance will return to the EMS center and, as consequence, the crew will be engaged for less time and more resources will be available. Related to this point, few works were found in the literature. For instance, [START_REF] Cerna | Machine learning-based forecasting of firemen ambulances' turnaround time in hospitals, considering the COVID-19 impact[END_REF] analyzes and predicts the spending time of an ambulance in a hospital to complete the transfer of the victim and return to its center. If these times are large or the workload is heavy, it can lead to breakdowns in the EMS [START_REF] Cerna | Predicting fire brigades operational breakdowns: A real case study[END_REF].

Although the collection of medical data allows investigations to propose improved ML-based decision-support tools, on the other hand, there is a problem with the disclosure of personal and sensitive information. Currently, data breaches are all too common [START_REF] Mccandless | World's biggest data breaches & hacks[END_REF], which in our context, would jeopardize both the victims' and operators' privacy. In addition, data breaches are not the only issue since ML models can also leak private information in an indirect way [START_REF] Song | Machine learning models that remember too much[END_REF], [START_REF] Shokri | Membership inference attacks against machine learning models[END_REF]. To solve these issues, in the privacy-preserving data mining literature, some works propose to train ML models with sanitized data [START_REF] Paul | An efficient perturbation approach for multivariate data in sensitive and reliable data mining[END_REF], [START_REF] Chamikara | Efficient data perturbation for privacy preserving and accurate data stream mining[END_REF], which is also known as input perturbation [START_REF] Kasiviswanathan | What can we learn privately?[END_REF].

We also adopt input perturbation because it allows using any ML and post-processing techniques in contrast with gradient [START_REF] Abadi | Deep learning with differential privacy[END_REF] or objective perturbation [START_REF] Chaudhuri | Differentially private empirical risk minimization[END_REF]. Besides, sanitizing the training dataset as we performed in this paper is in accordance with real-world applications where EMS would use and/or share only sanitized data with trusted third parties to train and develop ML-based decision support systems. This way, because each sample in the dataset is made private, data are protected from data leakage and are more difficult to reconstruct when the ML model receives attacks, for example. As shown in the results, it was still possible to achieve similar scores than when training ML models with the original data, which suggests that some patterns were kept even with the transformed QID features (cf. Fig. 4 and Fig. 5). More specifically, while the results with the k-anonymous dataset approximates the ones with original data, the results with DP decreased more. This could be due to DP applying both subsampling of the training dataset as well as the generalization and/or suppression of QIDs to satisfy K-Anon.

V. CONCLUSIONS AND PERSPECTIVES

This paper proposes a new ML-based methodology to predict both the victims' mortality and their need for transporta-


Jeremy Kuhn
email: jeremy.d.kuhn@gmail.com

A Dynamic Semantics for Multimodal Communication

Keywords: Iconicity, Dynamic semantics, Sign language, Cataphora, Multimodality

published or not. The documents may come   L'archive ouverte pluridisciplinaire

Introduction

Human communication expresses meaning both through description ('grammar') and depiction ('iconicity') [START_REF] Clark | Depicting as a method of communication[END_REF]. An English speaker may describe a scene with words and sentences at the same time as depicting it through co-speech gesture. In sign languages, description and depiction are arguably even more intertwined, with the signing space being used to iconically organize and depict referents that have been introduced in the discourse [START_REF] Goldin-Meadow | Gesture, sign and language: The coming of age of sign language and gesture studies[END_REF]. In this paper, focusing on data from French Sign Language (LSF), I argue that both descriptive and depictive meaning should be represented using dynamic semantics, in parallel but interacting systems.

Dynamic semantics provides a mechanism by which information and discourse referents are introduced gradually into context as a discourse unfolds [START_REF] Groenendijk | Dynamic predicate logic[END_REF]. Dynamic semantics involves left-to-right evaluation: discourse referents must be introduced before they can be accessed, as shown in [START_REF] Barker | Possessive descriptions[END_REF]. Anaphoric relations also depend on the local contexts introduced by logical operators; in [START_REF] Brasoveanu | Incremental and predictive interpretation: Experimental evidence and possible accounts[END_REF], for example, pronominal reference is possible only within the local context under nobody.

(1) Left-to-right evaluation a.

[A man] i entered the room. He i began to sing. b. * He i began to sing. [A man] i entered the room.

(2) Sensitivity to local contexts a.

Nobody received [a prize] i and bragged about it i . b. * Nobody recieved [a prize] i . It i was made of gold.

Here, I argue that a similar dynamic system governs the iconic use of space in sign language. Intuitively, one must create a picture before one can point to it. This dynamic iconic system runs parallel to the grammatical system, but interfaces with it. I motivate this by looking at a number of linguistic phenomena. First, I look at cases of cataphora, or 'backwards anaphora,' which have been claimed to be more restricted in sign language than in spoken language. Second, I look at indefinites appearing in embedded contexts, where iconic inferences are interpreted relative to the local context.

Depictive meaning

Descriptive and depictive representations over time

Consider how a series of linguistic utterances, unfolding over time, change a discourse representation. In (3), we start out with an empty context; (3a) introduces John into the discourse context; (3b) introduces Mary; (3c) introduces Susan. Linguistic expressions that predicate about these discourse referents establish semantic relations between them (see, call over ). As the discourse develops, these discourse referents can be referred to by pronouns.

(3) a. John entered.

b. Mary saw him. c.

She called Susan over.

Now consider how a pictorial production, unfolding over time, changes a discourse representation. In (4), we start out with an empty context; (4a) introduces A into the discourse context; (4b) introduces B; (4c) introduces x. Here, semantic relations are not introduced by linguistic expressions, but rather by holistic iconic mappings acting on the structural, configurational properties of the forms themselves: B is interpreted as a subset of A and x is interpreted as an element of A that is not in B. As the discourse develops, these discourse referents can be referred to, by the labels 'A,' 'B,' and 'x' that name the objects once they have been introduced, or by gestural pointing (in a multimodal setting).

(4) a.

b. c.

In either case, there is a mechanism to introduce discourse referents. There is a mechanism of predication (although descriptive relations and iconic relations are qualitatively different in nature). And there is a mechanism of indexicality or anaphoricity that allows the retrieval of discourse referents (but only those that have been introduced by that point in the discourse).

In multimodal utterances these two systems may interact. A speaker may point to a depicted object, and refer to it with linguistic anaphora, such as this, that or it. Iconic inferences may be generated about linguistically introduced discourse referents, via depictive elements (gestures, drawings, etc.) that cooccur with an utterance.

In what follows, I will show that sign language provides a rich case study to investigate the interaction of descriptive and depictive meaning. I will argue that the two different kinds of meaning can be productively seen as acting on two separate tiers of representation, with grammatical mechanisms that mediate between them. I will propose a model of the iconic level of meaning that draws heavily on recent theories of dynamic semantics, thus extending the theories that have been built for (3) to the representations manipulated in (4).

Spatial features in sign language

Sign languages are well known to use space to index discourse referents. A noun phrase may be established at a locus-a point in the horizontal space in front of the signer. Later, the signer may direct a pronoun to this locus to retrieve the relevant discourse referent. This use of space in sign language mirrors the use of logical variables, motivating some researchers to posit that loci are in fact a syntactic realization of variable names [START_REF] Lillo-Martin | Pointing out differences: ASL pronouns in syntactic theory[END_REF][START_REF] Schlenker | Donkey anaphora: the view from sign language (ASL and LSF)[END_REF].

On the other hand, [START_REF] Kuhn | ASL Loci: Variables or Features?[END_REF][START_REF] Kuhn | Disjunctive discourse referents in french sign language[END_REF] argue that loci are not themselves variables; rather, they act as morphological features that constrain the value of a pronoun. Specifically, [START_REF] Kuhn | ASL Loci: Variables or Features?[END_REF] observes that two pronouns may appear at the same locus but nevertheless receive different interpretations. For example, the LSF sentence in (5a) may receive a reading in which one pronoun co-varies under only but the other does not. Loci are thus closer in behavior to the gender features in (5b) than to the variable names in the logical form in (5c).

(5) a. only jean-a question poss-a mother poss-a favorite color.

' One implementation of this insight is as a presupposition on the value of the pronoun [START_REF] Schlenker | Featural variables[END_REF]. Following [START_REF] Jacobson | Towards a variable free semantics[END_REF], we define pronouns as the identity function. The feminine English pronoun she presupposes that the value returned is a female; by analogy, the LSF pronoun ix-a presupposes that the value returned is at locus a, as shown in [START_REF] Chierchia | Dynamics of meaning: Anaphora, presupposition, and the theory of grammar[END_REF]. What remains defined, of course, is what the meaning of a locus is and what it means for a value to be 'at' this locus. Below, I will argue that loci like 'a' are referents in a iconic, pictorial representation that grows as discourse develops. Like in standard theories of dynamic semantics, a pictorial discourse referent must be introduced before it can be retrieved. Additionally, the pictorial representation generates iconic inferences arising from a mapping that preserves structural properties of loci. Depending on context, these inferences may include rich geometric structure, such as the geometric configuration of individuals in a three dimensional space, schematic properties such as set relations, or very minimal structure, approximating a simple list of referents. For present purposes, we will assume only a single iconic constraint on loci: namely, a single individual cannot be at two different loci at the same time. 1 This entails that (a) a pronoun at one locus may not be bound by an antecedent at a different locus and, (b) the use of two loci entails the existence of two distinct discourse referents.

Cataphora and order sensitivity

As mentioned in the introduction, dynamic systems show order sensitivity: discourse referents must be introduced before they can be accessed, as in [START_REF] Clark | Depicting as a method of communication[END_REF].

(7) a.

[A man] i entered the room. He i began to sing. b. * He i began to sing. [A man] i entered the room.

If iconic representations are also governed by a dynamic system, then we should expect to see similar order sensitivity. Here, I argue that evidence in favor of such order sensitivity comes from examples involving cataphora, in which a pronoun precedes its binder. Notably, on the definition in (6b), there are two values to be bound-the value of the pronoun (x), and the value of the locus (a). Even when a pronoun is subject to quantificational, in-scope binding, the locus still requires dynamic binding of the iconic variable. I will argue that certain cases of cataphora allow a dissociation of these two levels. In these examples, quantificational binding of the pronoun proceeds as normal, but dynamic binding of the locus is no longer possible.

Cataphora as in-scope binding

Cataphora describes a phenomenon in which a pronoun precedes its binder, as shown in (8b).

(8) a.

Before Jean i left the office, he i turned out the lights. b.

Before he i left the office, Jean i turned out the lights.

Exactly what is going on in cases of cataphora has been the subject of some discussion [START_REF] Brasoveanu | Incremental and predictive interpretation: Experimental evidence and possible accounts[END_REF][START_REF] Chierchia | Dynamics of meaning: Anaphora, presupposition, and the theory of grammar[END_REF]. One particular point of note regards the nature of binding in these examples: is it quantificational binding or dynamic binding? I think that a reasonable case can be made that at least some of these examples are cases of quantificational, in-scope binding. First, cataphora is becomes extremely degraded across sentence boundaries, as [START_REF] Graf | Is syntactic binding rational?[END_REF]. This suggests that the binding relation in (8b) arises from sentence-internal mechanisms.

(9) a.

Jean i left the office. He i forgot to turn out the lights. b. * He i left the office. Jean i forgot to turn out the lights.

Second, at least some cases of cataphora allow binding by quantificational expressions, including negative quantifiers, as in [START_REF] Groenendijk | Dynamic predicate logic[END_REF]. These facts suggest that the subordinate clause in these examples is interpreted at a lower position (possibly adjoined to the verb phrase), where the pronoun is in the scope of the quantificational expression.

(10) a. When his i child throws a tantrum, [no father] i can sit idly by.

b. Unless they i bought it j in the last year, [none of my relatives] i own [a gun] j .

Iconic constraints on cataphora in sign language

Interestingly, it has been remarked occasionally that cataphora (or 'backwards anaphora') is significantly less available in sign language than it is in a spoken language like English [START_REF] Van Hoek | Anaphora and conceptual structure[END_REF][START_REF] Sandler | Sign language and linguistic universals[END_REF][START_REF] Koulidobrova | A 'point' of inquiry: The case of the (non-) pronominal IX in ASL[END_REF]. An example from LSF is provided in [START_REF] Van Hoek | Anaphora and conceptual structure[END_REF].

The syntactic structure is equivalent to the grammatical English example in (8); however, the LSF sentence becomes ungrammatical when an overt pronoun points to a locus where the antecedent will later be introduced, in (11b).

(11) a. jean-a leave office before, ix-a light-off 'Before Jean left the office, he turned out the lights.' b. * ix-a leave office before, jean-a light-off Intended: 'Before he left the office, Jean turned out the lights.'

Koulidobrova and Lillo-Martin (2016) offer an informal explanation of this observation: one can't point to something (an object or a demonstration) until it has been introduced. This is exactly the constraint on iconcity that we aim to spell out in dynamic terms.

Expressing this as a constraint on space and iconicity makes a further prediction. Specifically, cataphora should sometimes be possible in LSF, but only in cases in which a non-iconic pronominal form is used. This prediction seems to be borne out. First, LSF (like a number of other sign languages) allows the use of null pronouns in certain positions. As observed by [START_REF] Schlenker | Donkey anaphora: the view from sign language (ASL and LSF)[END_REF], since null pronouns have no overt form, they generate no iconic inferences and cannot be subject to iconic constraints. As seen in [START_REF] Jacobson | Towards a variable free semantics[END_REF], null pronouns also do allow cataphora. Second, some relational nouns have been argued to involve implicit anaphora (neighbor = 'neighbor of x') [START_REF] Partee | Binding implicit variables in quantified contexts[END_REF][START_REF] Barker | Possessive descriptions[END_REF]. Unlike pronouns, these nouns allow a neutral form that does not invoke any iconic use of space; for example, the sign neighbor in ( 13) is signed in the neutral space in front of the signer. As seen in ( 13), the interpretation of the sentence allows a cataphoric relation, in which the implicit argument is bound by the later noun phrase.2 [START_REF] Jacobson | Towards a variable free semantics[END_REF] leave office before, jean-a light-off 'Before he left the office, Jean turned out the lights.' (13) when neighbor noise, marie-a call police 'When (her) neighbor makes noise, Marie calls the police.'

These examples provide further evidence that the unavailability of cataphora in examples like [START_REF] Van Hoek | Anaphora and conceptual structure[END_REF] arises from the use of space and iconicity.

Analysis: Cataphora with iconicity

Based on the evidence in Section 3.1, we analyze our examples of cataphora as in-scope, quantificational binding. Specifically, we assume that a sentence with an adverbial phrase has an underlying structure in which the antecedent c-commands the pronoun that it binds. A syntactic operation dislocates the temporal phrase to the left, but a mechanism of reconstruction allows the pronoun to be interpreted in its lower position, bound by its antecedent.

To this static analysis, we add a dynamic component that manages the pictorial representation. That this representation is pictorial, and not just a list of discourse referents, will be seen in the fact that iconic inferences can be drawn the geometric relations between the locations in space. In the example below, though, only a single discourse referent is established in the dynamic picture, so no iconic inferences appear. The present system is thus for the moment highly similar to a standard dynamic semantics that manages discourse referents.

Building on [START_REF] Charlow | On the semantics of exceptional scope[END_REF][START_REF] Bumford | Incremental quantification and the dynamics of pair-list phenomena[END_REF] meaning is modeled as a tuple which pairs the basic static meaning of an expression with its dynamic effect on the pictorial representation that is being constructed in context. For linguistic expressions that make no reference to this representation, their static meaning x can be converted to a dynamic type via the unit operator η in [START_REF] Kuhn | ASL Loci: Variables or Features?[END_REF], which passes along a pictorial representation unchanged. ( 14) η(x) = λP. x, P We note that one formal difference between this model and standard dynamic models is that there is no nondeterminism. In linguistic utterances, indefinites like somebody can introduce discourse referents whose value varies across a set of assignment functions. In contrast, pictures are always definite, so only a single pictorial representation is needed at any given stage of the computation.

In iconic constuctions, when noun phrases and pronouns are indexed in space, they manipulate or make reference to the pictorial representation. Noun phrases at loci introduce a new pictorial discourse referent, then presuppose that the relevant individual is at pictorial referent, as shown in [START_REF] Kuhn | Logical meaning in space: Iconic biases on quantification in sign languages[END_REF]. Pronouns do not change the pictorial representation, but presuppose that the value that they return is at the indicated pictorial referent, as shown in ( 16). ( 15) jean-a = λP. j if at(a)(j) in P+a # otherwise , P + a ( 16) ix-a = λP. λx.x if at(a)(x) in P # otherwise , P

The rules of composition are defined to pass dynamic information from left to right. Following [START_REF] Bumford | Incremental quantification and the dynamics of pair-list phenomena[END_REF], we define these rules directly, but see [START_REF] Charlow | Static and dynamic exceptional scope[END_REF] for discussion about how to define them in terms of an applicative functor. Critically, in these definitions, regardless of whether a function appears to the left or the right of its argument, the pictorial information is updated first by the element on the left and then by the element on the right. x, P = m(P)

As an example, consider an LSF sentence with an overt cataphoric pronoun. Since the subordinate clause appears linearly first, it updates the iconic representation first, via the definitions in [START_REF] Lillo-Martin | Pointing out differences: ASL pronouns in syntactic theory[END_REF]. The resulting meaning is provided in [START_REF] Partee | Binding implicit variables in quantified contexts[END_REF]. Of note, because the pronoun is evaluated before locus a has been introduced, the meaning presupposes that the value of the pronoun (Jean) is at a in the input context P. This presupposition is not satisfied, so the sentence is infelicitous. [14] evaluates a hypothesis, very similar to the one proposed here, on which loci introduce a presupposition that constrains the full range of values that can be taken by a pronoun. The hypothesis is stated in [START_REF] Sandler | Sign language and linguistic universals[END_REF].

(19) Referential locus hypothesis: In a context c, the value of a locus is provided by the assignment function g c , where g c (i) is the set of type e, t that corresponds to the noun indexed at locus i in c.

a. ∀ assignment functions s, ix-i k = s(k) if s(k) ∈ g c (i); # otherwise [14, p . 455]
[14] ultimately rejects this hypothesis, however, based on examples in ASL in which two quantified expressions range over the same set of individuals. Empirically, [START_REF] Kuhn | ASL Loci: Variables or Features?[END_REF] observes that the two quantifiers in ( 20)-( 21) may both range over the same set of individuals; in [START_REF] Schlenker | Local contexts[END_REF], for example, John may be either the helper or the person helped. If loci introduce a global presupposition on the values that a pronoun can take, this means that the presupposition introduced by locus a and locus b will be identical, since g c (a) = g c (b). And, if ix-a and ix-b carry exactly the same presupposition, then a pronoun at either locus is predicted to be ambiguous. But this prediction is not borne out: pointing to locus a or locus b does disambiguate the sentence. I contest that the source of this problem is that the presupposition in ( 19) is taken to be a constraint on the global context. A related presupposition, such as the one I have proposed in (6b), can avoid these pathological predictions if we relativize the presupposition to the local context of the locus.

Local contexts in dynamic semantics

A local context describes the immediate scope in which an expression is interpreted. This includes information from the global context (roughly, the common ground), but also incorporates information about the syntactic environment in which the expression appears [START_REF] Schlenker | Local contexts[END_REF].

For non-iconic phenomena, constraints related to discourse reference have been shown to be sensitive to the local context. The simplest such constraint is that a pronoun can only be used in a context in which it has a non-empty value. For example, as foreshadowed in the introduction, the pronoun in (22a) cannot be anaphoric to the indefinite a prize, since the context in which it appears entails that there is no such object. This, however, does not mean that no such discourse referent is introduced-indeed, a pronoun within the scope of nobody can refer back to it felicitously, as in (22b). In its local context, this pronoun has a non-empty value. Similarly, the adjectives other and else presuppose the existence of another individual-but once again, this is evaluated with respect to the local context. Examples ( 23)-( 25) illustrate the point. In (23), the two indefinites are unembedded, so the local context and the global context are the same; the sentence entails that there are two boys, one who coughed and one who laughed. In examples with embedding, though, the local context and global context differ, generating different judgments. In (24a), for example, another American is interpreted in the scope of the when clause; in this local context, the existence of another American has been entailed, so the presupposition of another is satisfied. In contrast, in (24b), another American appears in the following sentence, in a global context which does not entail the existence a first American; the sentence is thus degraded. Similarly, in (25a), every other boy is interpreted in the distributive scope of every boy, a local context which entails the existence of another boy. In the global context, the two quantified expressions can thus range over the same set of individuals. But in (25b), when every other boy appears in the following sentence, other must be interpreted with respect to the global context, so the only interpretation is one in which the there are two distinct groups of boys, one which coughed and one which laughed.

(23) One boy coughed. Another boy laughed.

(24) a.

When an American sees another American, they say hi. b. ? When an American goes to Paris, they take a lot of pictures. When another American goes to Paris, they go to the Louvre.

(25) a. Every boy told every other boy that he would win. b. ? Every boy coughed. Every other boy laughed.

Local contexts for iconicity

Parallels with the English examples in (24a) and (25a) can help us understand the ASL examples in [START_REF] Schlenker | Local contexts[END_REF] and [START_REF] Schlenker | Donkey anaphora: the view from sign language (ASL and LSF)[END_REF]. As discussed in Section 2.2, we have been assuming a rather weak iconic inference-namely, that the use of two loci entails that there are two distinct individuals. By analogy with the English examples, it is clear that this is satisfied in the local contexts for both of the ASL sentences.

On the other hand, because this iconic inference is so weak, it is impossible to dissociate it from inferences that already arise from [START_REF] Schlenker | Local contexts[END_REF] and [START_REF] Schlenker | Donkey anaphora: the view from sign language (ASL and LSF)[END_REF]. Specifically, the existence of two distinct individuals is already strongly implicated by [START_REF] Schlenker | Local contexts[END_REF] and is entailed by the word other in [START_REF] Schlenker | Donkey anaphora: the view from sign language (ASL and LSF)[END_REF], independent of the use of loci.

In order to isolate the contribution of the iconic inference, and its modulation by the local context, we can thus consider new examples in which the use of two indefinites does not independently implicate the existence of two individuals. The sentences in (26) provide one such example, in which the signer is explaining the rules of a card game. In (26a), the same locus is used twice; in (26b), two distinct loci are used. In both (26a) and (26b), the values of someone range over the set of all individuals; the use of space thus does not introduce any global constraints on the interpretation of these pronouns. However, within the local context introduced by the conditional if, there is an iconic inference. When two distinct locations in space are used, the two discourse referents must be distinct. In (26a), the person who loses may or may not be the person who drew the card; in contrast, (26b) entails that the person who loses is not the person who drew the card. Iconic inferences thus exist, but they, like the presupposition of other, are evaluated with respect to the local context.

(26) Context: Explaining the rules of a card game a. if someone-a draw ix snake, someone-a lose. 'If someone draws the snake card, someone loses.' b. if someone-a draw ix snake, someone-b lose 'If someone draws the snake card, someone else loses.'

Finally, we note that [START_REF] Kuhn | Logical meaning in space: Iconic biases on quantification in sign languages[END_REF] argues that, while it is not obligatory, there is often a tendency to interpret iconicity with respect to the global context. Such an inference may have a variety of effects, including a preference to avoid bound pronouns under negative quantifiers when other strategies are available [START_REF] Graf | Is syntactic binding rational?[END_REF], or the preference of some signers to interpret [START_REF] Schlenker | Donkey anaphora: the view from sign language (ASL and LSF)[END_REF] as referring two groups of students, analogous to the interpretation of (25b) [START_REF] Kuhn | ASL Loci: Variables or Features?[END_REF].

Conclusion

Drawing on a number of sign language phenomena in which grammatical operations intersect with iconicity, I have argued that iconic representations are governed by a dynamic system that is order-sensitive and mediated by local contexts. I have provided an explicit proposal in which descriptive and depictive meaning are represented in parallel but interacting systems, which thread a growing iconic representation through the discourse.

( 6 )

 6 a. she = λx : fem(x) . x b. ix-a = λx : at(a)(x) . x

  (x), P where x, P = n(P ) f, P = m(P) b. B B\A → A m n λP. f (x), P where f, P = n(P )

( 18 ), P + a 4 Iconicity and local contexts 4 . 1

 18441 ix-a leave office before, jean-a light-off = λP. light-off(j) before leave(j) if at(a)(j) in P and at(a)(j) in P+a # otherwise The problem with presuppositions on the global context

( 20 )

 20 when someone-a help someone-b, ix-b happy 'When someone helps someone, he [=the latter] is happy.' (21) [all boy]-a tell [all other boy]-b ix-a will win 'Every boy told every other boy that he [=the former] would win.' (ASL; [14, p. 456])

( 22 )

 22 a. * Nobody recieved [a prize] i . It i was made of gold. b.Nobody received [a prize] i and bragged about it i .

We leave it open whether this is an entirely iconic constraint that can be weakened in appropriate contexts, or whether there is also a stricter constraint that requires morphosyntactic feature matching; of relevance, see[START_REF] Schlenker | Featural variables[END_REF] on bound iconic loci.

In some cases, this interpretation may compete with an interpretation in which the implicit argument is interpreted as the signer-for example sister = 'my sister.'

The research leading to these results received funding from ERC H2020 Grant Agreement No. 788077-Orisem (PI: P. Schlenker). Research was conducted at the Département d'Etudes Cognitives (ENS), which is supported by ANR-17-EURE-0017 FrontCog.


O Rance

N Barbot #

E Perret

Comparison between Cross-polarization and Circular Polarization Interrogation for Robust Chipless RFID Reading

Keywords: Radar Cross Section, Circular polarization, chipless RFID, polarimetric scattering matrix

Circular polarization for chipless tag interrogation has recently been presented as an improvement over the conventional cross-polarization method as it is supposed to be both orientation-independent and able to isolate the tag from its environment. In this article, we make a systematic comparison between the two approaches. We show, from both theory and measurements, that for the circular polarization approach, the assumptions of orientation independence and isolation are valid only for very specific and non-realistic environments. A new tag has been used for the characterization. It can be manufactured by hand in less than five minutes at negligible cost and yet has performances comparable to optimized tags, making it ideal for rapid prototyping.

I. INTRODUCTION

The radar signature of a chipless RFID tag is generally very small compared to that of the surrounding objects. A classical technique [START_REF] Vena | A depolarizing chipless RFID tag for robust detection and its FCC compliant UWB reading system[END_REF] to separate these two contributions is the use of a depolarizing tag (dipoles oriented at 45°) combined with a cross-polarization interrogation, as shown in Fig. 1a. This method is considered the most robust at present but requires knowledge of the orientation of the tag.

One possible improvement path is the use of a circularly polarized (CP) wave for interrogation (Fig. 1b), which would make the reading independent of orientation. This approach has been presented in two recent studies, but both have limitations. In [START_REF] Martinez | Circular polarization on depolarizing chipless RFID tags[END_REF], the authors show rotational invariance in measurement for only three different angles and do not present a theory to support this assertion. Moreover, they do not show the impact of the environment in measure. In [START_REF] Genovesi | Orientation-insensitive and normalization-free reading chipless RFID system based on circular polarization interrogation[END_REF], the authors show the rotational invariance only in simulation (in the absence of environment) and the robustness of reading is shown in measurement only for a single environment consisting of a square metal plate. That environment, despite having a high RCS in co-polarization, will be proven to be a favorable case.

In this paper, we will first establish the theoretical link between the two approaches, which will allow us to rigorously justify the invariance and isolation hypotheses as well as their limits. These two hypotheses will be tested in measurement. II. THEORY A very powerful tool for the analysis of scatterers is the polarimetric scattering matrix (PSM) [START_REF] Knott | Radar Cross Sections[END_REF] which was introduced during the early development of radar. The PSM relates the incident and reflected electric field at the target, component by component, and makes it possible to calculate analytically the dependence on the orientation 𝜃𝜃 (angle with respect to vertical) using [START_REF] Knott | Radar Cross Sections[END_REF]:

𝑺𝑺(𝜃𝜃) = � cos 𝜃𝜃 sin 𝜃𝜃 -sin 𝜃𝜃 cos 𝜃𝜃 � • � 𝑆𝑆 𝑣𝑣𝑣𝑣 𝑆𝑆 𝑣𝑣ℎ 𝑆𝑆 ℎ𝑣𝑣 𝑆𝑆 ℎℎ � • � cos 𝜃𝜃 -sin 𝜃𝜃 sin 𝜃𝜃 cos 𝜃𝜃 �. (1)
The PSM can be defined for either linear or circular polarization (denoted 𝑺𝑺 and 𝑺𝑺 𝒄𝒄 respectively) and the relation between the two is given by a simple change of basis [START_REF] Knott | Radar Cross Sections[END_REF]: where l and r stand for lefthand and righthand polarizations and v and h stand for vertical and horizontal. Table 1 gives the PSM of reference targets as a function of the orientation 𝜃𝜃 for both linear and circular polarizations calculated from ( 1) and ( 2). Before analyzing each scatterer individually, it is worth noting that the components of 𝑺𝑺 exhibit dependence on 𝜃𝜃 in both magnitude and phase, while only the phase of the components of 𝑺𝑺 𝒄𝒄 is influenced by 𝜃𝜃. The total backscattered E-field is generally a complex sum between a tag for which 𝜃𝜃 can be varied and a static environment (with static orientation 𝜃𝜃 0 ):

� 𝑆𝑆 𝑙𝑙𝑙𝑙 𝑆𝑆 𝑟𝑟𝑙𝑙 𝑆𝑆 𝑙𝑙𝑟𝑟 𝑆𝑆 𝑟𝑟𝑟𝑟 � = � 1 -𝑗𝑗 1 j � • � 𝑆𝑆 𝑣𝑣𝑣𝑣 𝑆𝑆 𝑣𝑣ℎ 𝑆𝑆 ℎ𝑣𝑣 𝑆𝑆 ℎℎ � • � 1 1 -j 𝑗𝑗 �, (2)
𝑺𝑺 𝑐𝑐 tot (𝜃𝜃) = 𝑺𝑺 𝑐𝑐 tag (𝜃𝜃) + 𝑺𝑺 𝑐𝑐 env (𝜃𝜃 0 ) (3)
And it becomes evident that the magnitude of the total signal varies with 𝜃𝜃 due to the possible recombination of the respective phases. The hypothesis of rotational invariance is therefore not valid for CP in presence of an environment. The first row (R1) of table 1 presents the PSM of a dipole. We see that, as expected by both techniques, the tag has a maximum cross-polarization 𝑆𝑆 𝑣𝑣ℎ for 𝜃𝜃 = 45° and also has a non-zero 𝑆𝑆 𝑙𝑙𝑙𝑙 component. We now consider the second row R2 which corresponds to an ideal environment for which the approximation of optical reflection is valid. Note that the same scattering matrix is obtained for a planar target having n-fold symmetry with n>2 [START_REF] Mackay | Proof of polarisation independence and nonexistence of crosspolar terms for targets presenting n-fold (n>2) rotational symmetry with special reference to frequency-selective surfaces[END_REF], which is the case for the environment chosen in [START_REF] Genovesi | Orientation-insensitive and normalization-free reading chipless RFID system based on circular polarization interrogation[END_REF]. In this case we see that the components 𝑆𝑆 𝑣𝑣ℎ and 𝑆𝑆 𝑙𝑙𝑙𝑙 are both null, so that it should not introduce any perturbations for the reading techniques presented in Fig. 1. However in most cases it is not possible to approximate the environment using R2. A more realistic environment can be represented with the case 𝑆𝑆 𝑣𝑣𝑣𝑣 ≠ 𝑆𝑆 ℎℎ which corresponds to R3. In this case, 𝑆𝑆 𝑣𝑣ℎ and 𝑆𝑆 𝑙𝑙𝑙𝑙 are not zero, implying that the environment disturbs the measurement of the tag for both techniques. However, the environment is predominantly composed of vertical or horizontal objects, so that it is usually possible to consider that 𝜃𝜃 0 = 0° or 𝜃𝜃 0 = 90°, which leads to a cancellation of 𝑺𝑺 but not 𝑺𝑺 𝒄𝒄 . The perturbation introduced by the environment is thus usually weak for the cross-polarization approach, while it remains important for the circular polarization. The special case 𝑆𝑆 𝑣𝑣𝑣𝑣 = 𝑆𝑆 ℎℎ represents an important operational constraint and is rarely encountered in practice.

III. MEASUREMENTS

A. Tag and Measurement Setup

It is not necessary to precisely control the resonance frequency of the dipoles to characterize the reading method. We therefore propose a new rapid prototyping method which simply consists in cutting sections of electrical wires (H07VU 2.5 mm²) which are then taped on a square ground plane as shown in Fig. 2. The insulating PVC sheath of the electrical Fig. 2. Picture of the tag made by taping sections of electrical wires to a ground plane. This rapid prototyping method gives comparable performances to optimized tags realized by chemical etching on RF materials [START_REF] Vena | A depolarizing chipless RFID tag for robust detection and its FCC compliant UWB reading system[END_REF].

Scatterer type

𝑺𝑺(0)

𝑺𝑺(𝜃𝜃) calculated using (1) 𝑺𝑺 𝒄𝒄 (𝜃𝜃) calculated using ( 1) and ( 2)

R1 Dipole like scatterer 𝑎𝑎 � 1 0 0 0 � 𝑎𝑎 � cos² 𝜃𝜃 -sin 𝜃𝜃 cos 𝜃𝜃 -sin 𝜃𝜃 cos 𝜃𝜃 sin² 𝜃𝜃 � 𝑎𝑎 2 � 𝑒𝑒 𝑗𝑗2𝜃𝜃 1 1 𝑒𝑒 -𝑗𝑗2𝜃𝜃 � R2 Specular reflexion (ideal environment) 𝑎𝑎 � 1 0 0 1 � 𝑎𝑎 � 1 0 0 1 � 𝑎𝑎 � 0 1 1 0 � R3 Non specular reflexion (realistic environment) � a 0 0 𝑏𝑏 � � 𝑎𝑎 cos² 𝜃𝜃 + 𝑏𝑏 sin² 𝜃𝜃 (𝑏𝑏 -𝑎𝑎) sin 𝜃𝜃 cos 𝜃𝜃 (𝑏𝑏 -𝑎𝑎) sin 𝜃𝜃 cos 𝜃𝜃 𝑏𝑏 cos² 𝜃𝜃 + 𝑎𝑎 sin² 𝜃𝜃 � � (𝑎𝑎 -𝑏𝑏)𝑒𝑒 𝑗𝑗2𝜃𝜃 𝑎𝑎 + 𝑏𝑏 𝑎𝑎 + 𝑏𝑏 (𝑎𝑎 -𝑏𝑏)𝑒𝑒 -𝑗𝑗2𝜃𝜃 �
wire ensures a good spacing between the different resonators as well as with the ground plane. This configuration, which does not use any specific RF material, makes it possible to produce microstrip resonators in less than 5 min with almost negligible cost and good coding density. The resonators made in this way (Fig. 2) have a comparable RCS and a selectivity that is even higher than tags that have been optimized and realized by chemical etching on RF materials [START_REF] Vena | A depolarizing chipless RFID tag for robust detection and its FCC compliant UWB reading system[END_REF]. The scattering matrix of the resonators is given by R1 in table 1.

The measurement setup is shown in Fig. 3a. We used the same QH 800 antenna with ports V and H connected either directly to the VNA (Agilent Technologies PNA 5222A) for cross polarization measurement or to a quadrature hybrid coupler (QH0226) for circular polarization measurement. For the CP configuration, we obtain an axial ratio inferior to 1.5 dB and a cross-polarization ratio superior to 21 dB. The tag is placed 20 cm from the antennas in a semi-anechoic environment (modified starlab).

B. Effect of the Orientation

The first series of measurement shows the influence of orientation on the tag signature. The tag, whose dipoles are initially oriented at 45° in order to maximize the crosspolarization components, is rotated from 0° to 90° by steps of 10°. The orientation of the tag is manually modified with a precision of approximately 2°. For linear polarization (Fig. 4a), a 45° signal cancellation is observed for all dipoles, which is theoretically expected according to [START_REF] Vena | A depolarizing chipless RFID tag for robust detection and its FCC compliant UWB reading system[END_REF]. For the circular polarization (Fig. 4b), there is no cancellation and the signal appears to be relatively independent of the angle (a maximum variation of 3.8 dB is observed for the Res2 for a 25 dB peak). It should be noted, however, that the ground plane of the tag has been integrated into the reference measurement and subtracted from the tag measurement in Fig. 4. If not, the total backscattered signal is the complex sum between the broadband signal of the ground plane and the resonant signal of the microstrip dipoles [START_REF] Genovesi | Orientation-insensitive and normalization-free reading chipless RFID system based on circular polarization interrogation[END_REF]. In such a case, the resonances are observable whatever the angle but sometimes in the form of a peak and sometimes in the form of a dip due to phase recombination.

C. Effect of the Environment

For the analysis of the influence of the environment, we consider five different environments (Fig. 3b) which are positioned 5 cm behind the tag (Fig 3c). For linear polarization (Fig. 5a), the environment has only a limited influence on the tag signature with a maximum variation compared to the tag alone of 2 dB on Res4 for Env. 2, which is the one with the largest cross-polarization magnitude. On the other hand, it is clear that the signature of the tag is strongly influenced by the environment for circular polarization (Fig. 5b). Although perturbed, the tag identifier remains readable for environments 1 and 2. For env. 3 to 5, which have a higher RCS in copolarization, the signature can no longer be decoded.

IV. CONCLUSION

In this paper, we have tested the hypotheses of rotational invariance and isolation for the circular polarization reading method. The method can be considered invariant by rotation for a tag measured in semi-anechoic condition and a wellchosen ground plane shape (R2 of table 1) but not for real environment. It was also found that the method cannot be considered as an improvement of [START_REF] Vena | A depolarizing chipless RFID tag for robust detection and its FCC compliant UWB reading system[END_REF] in terms of reading robustness because it is highly impacted by environment.

Fig. 1 .

 1 Fig. 1. (a) Cross-polarization interrogation technique [1]. The PSM of the tag has a non-zero cross-component 𝑆𝑆 𝑣𝑣ℎ , which is not the case for classical objects. (b) Circular polarization approach [2-3]. The PSM of the tag has a non-zero component with same handedness (e.g. 𝑆𝑆 𝑙𝑙𝑙𝑙 ), which is not the case for classical objects.

Fig. 3 .

 3 Fig. 3. (a) Picture of the measurement setup. Monostatic measurement in semi-anechoic environment. (b) Different surrounding scatterers used for environment. The scatterers are numbered by increasing RCS level. (c) Surrounding scatterer positioned 5 cm behind the tag.

Fig. 4 .

 4 Fig. 4. Measurement results of the tag signature as a function of orientation 𝜃𝜃 for (a) linear and (b) circular polarization.

Fig. 5 .

 5 Fig. 5. Measurement results of the tag in presence of different environments for (a) linear and (b) circular polarization. Env. 0 stands for the tag alone.

Table 1 .

 1 Polarimetric scattering matrix of classical targets as a function of the orientation θ for both linear and circular polarizations.

ACKNOWLEDGMENT This work is funded by the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation program (Grant No 772539, SCATTERERID).