Hafida Mouhagir
email: hafida.mouhagir@hds.utc.fr

⇤⇤ Reine Talj
email: reine.talj@hds.utc.fr

Véronique Cherfaoui
email: veronique.cherfaoui@hds.utc.fr

⇤ François
email: françois.aioun@mpsa.com

Aioun ⇤⇤

Franck Guillemard
email: franck.guillemard@mpsa.com

TRAJECTORY PLANNING FOR AUTONOMOUS VEHICLE IN UNCERTAIN ENVIRONMENT USING EVIDENTIAL GRID

Keywords: Autonomous vehicle, Path planning, Evidential occupancy grid

This paper considers the path planning problem for an autonomous vehicle given uncertain knowledge about the surrounding environment. We propose to use evidential occupancy grid to deal with sensor uncertainties. Our aim is to develop a planning approach based on clothoid tentacles allowing a vehicle to move autonomously and safely in an environment which is not perfectly known a priori and in which static obstacles are present.

INTRODUCTION

Whether driving on highways or exploring in the middle of a war zone, autonomous vehicles must have the capacity to rapidly and robustly planify a trajectory in very uncertain environment. The uncertainty comes from : imperfect knowledge of the vehicle model [START_REF] Xu | Motion planning under uncertainty for on-road autonomous driving[END_REF], environment sensing and environment predictability [START_REF] Aoude | Threat-aware path planning in uncertain urban environments[END_REF][START_REF] Sun | Trajectory planning for vehicle autonomous driving with uncertainties[END_REF]]. To solve environment predictability, Partially Observable Markov Decision Process (POMDP) [START_REF] Foka | Real-Time Hierarchical POMDPs for Autonomous Robot Navigation[END_REF][START_REF] Brechtel | Probabilistic decision-making under uncertainty for autonomous driving using continuous POMDPs[END_REF][START_REF] Gindele | Learning driver behavior models from tra c observations for decision making and planning[END_REF]] o↵ers a framework for autonomous robot navigation in dynamic environments. With this approach, the state of a car's environment can be estimated and the development of tra c situations can be predicted. In [Bonnin and Kummert 2012], the authors present a system able to predict the future behavior of the egovehicle in an inner-city environment; based on a manually constructed decision tree, the developed system recognizes the class of the situation that a tra c participant is facing. This approach doesn't predict other vehicles position or heading and their future directions which is vital in motion planning.

This paper addresses problems involving uncertainty in sensing and how to integrate this uncertainty in trajectory planning. For the autonomous vehicle applications, the perception system serves to model the environment in the proximity of the host vehicle. For modeling the environment, the occupancy grids have become the dominant paradigm for environmental modeling in mobile robotics. An occupancy grid map is a tessellated grid in which each cell stores fine grained, quantitative information regarding which areas of a robots operating environment are occu-pied and which are empty. Specifically, each individual cell in the grid records a confidence factor that the particular cell is occupied. Such maps are extremely useful for mobile robotic applications as they facilitate tasks such as navigation, path planning, localization and collision avoidance.

The main challenge in implementing the grid-based approach is how to deal with the uncertainties originating from the imprecise sensor readings, imprecise prior information and absence of information. In the literature, the Bayesian framework is the most popular method to tackle this problem by representing the uncertainties by means of probability as in [START_REF] Elfes | Using occupancy grids for mobile robot perception and navigation[END_REF][START_REF] Coue | Bayesian occupancy filtering for multitarget tracking: an automotive application[END_REF][START_REF] Adarve | Computing occupancy grids from multiple sensors using linear opinion pools[END_REF]. This framework has the advantages of being simple thus fast to implement. In recent years, the framework of belief function to deal with uncertainties gathers more and more attentionIt is a generalisation of the Bayesian framework. Thus a new branch of constructing the perceptual grids which is called evidential approach becomes another research hotspot. The approach was proposed in [START_REF] Pagac | An evidential approach to map-building for autonomous vehicles[END_REF]] to interpret sonar data into grid values, while in [START_REF] Yang | Evidential mapping for mobile robots with range sensors[END_REF][START_REF] Moras | Evidential perception grids for robotics navigation in urban environment[END_REF][START_REF] Yu | An evidential sensor model for velodyne scan grids[END_REF]] the authors used this framework for lidar sensors. According to the reported results one can remark that this approach brings new features to the mapping process: applications oriented combination operators for information fusion, new method of the management of conflict information, and flexible decision making methods.

In this paper, we propose to deal with uncertainty of environment sensing by using the information provided by evidential grid to choose the best trajectory to execute. The path planning part is based on the clothoid tentacles approach detailed in [START_REF] Mouhagir | A markov decision processbased approach for trajectory planning with clothoid tentacles[END_REF]].

The paper is organized as follows: Section 2 presents the concept of evidential grids. In Section 3, we explain how to consider the uncertainty in evidential grids in trajectory planning with tentacles. The simulation results based on data taken from SCANeR™Studio simulator are discussed in Section 4 . Finally, conclusions and perspectives are given is Section 5.

EVIDENTIAL OCCUPANCY GRID

The evidential occupancy grids gather more and more attention in the literature. In [START_REF] Pagac | An evidential approach to map-building for autonomous vehicles[END_REF][START_REF] Yang | Evidential mapping for mobile robots with range sensors[END_REF], the authors adopt the evidential approach to deal with uncertainties for perception grids. All these works report some performance improvements or some new features. Another interesting point is that di↵erent sensors are used in these works, sonars, lidars, etc, proving the e ciency and e↵ectiveness of the evidential occupancy mapping approach. Each cell of an evidential occupancy grid is a mass function (or belief function) giving the belief on occupancy.

Evidential framework

The theory of belief functions, also known as Dempster-Shafer theory (DST), was proposed by Dempster [START_REF] Dempster | Upper and lower probabilities induced by a multivmulti mapping[END_REF]], and developed, among others, by Shafer [START_REF] Shafer | A mathematical theory of evidence[END_REF]] and Smets [START_REF] Smets | Decision making in the tbm: the necessity of the pignistic transformation[END_REF]]. This formalism gained its popularity thanks to various interesting properties. DST not only generalizes the probability theory, but the possibility theory as well.

In the theory of Dempster-Shafer, a frame of discernment ⌦ is defined to model a specific problem. In the occupancy grid framework, the frame of discernment is defined as: ⌦ = {O, F }, referred as the states (occupied or free) of each cell. The power set is defined as 2 |⌦| = {;, F, O, ⌦}, with | ⌦ | is the cardinality of the set.

For quantitatively supporting the cell states, a mass function (also referred as basic belief assignment BBA) is calculated and provides four beliefs [m(F ) m(O) m(⌦) m(;)], where m(A) represents respectively the quantity of evidence that the space is F ree , Occupied , Unknown or Conf lict .

The function m returns values in the range of [0, 1] and satisfies the condition:

X A✓⌦ m(A) = 1 m(Ø)=0
, for a normalized mass function.

A powerful application of evidential theory is the fusion of di↵erent sources of information. The following section presents some combination rules.

Combination rules

The combination rules enable to fuse information from di↵erent sources. Herein, the sources of information should be defined in the same frame of discernment to use the following rules.

The Transferable Belief Model (TBM) conjunctive rule and Dempster's rule are noted \ and , respectively. They are defined as follows: Let m 1 and m 2 be two given mass functions describing the occupancy belief of the same cell, and let m 1 \ m 2 and m 1 m 2 be the result of their combination by \ and . We have:

m 1\2 (A) = X B\C=A m 1 (B)m 2 (C) , 8A ✓ ⌦ (1)
and, assuming that m 1\2 (Ø) 6 = 1:

m 1 2 (A) = 8 < : 0 if A = Ø m 1\2 (A) 1 m 1\2 (Ø) otherwise (2)
The normalization process in Dempster's rule has the e↵ect of distributing the belief from the conflict to the other propositions, according to their respective mass.

Evidential occupancy grids

We consider in the following the ego-centered evidential grids built from the sensor model described in [START_REF] Moras | Credibilist occupancy grids for vehicle perception in dynamic environments[END_REF]. This approach uses two grids. The ScanGrid is created from sensor data, Lidar points provide information about the state of the scanned cells. The masses assignment respects the least commitment principle : the cells containing a lidar point are occupied, the cells between the sensors and the occupied cells are free and the other are unknown The value of masses depends of the resolution of the grids and sensor performances. The second grid is the MapGrid that fuses the new ScanGrid at each perception step. The fusion rule is based on the conjunctive rule that can provides conflicting mass. The conflicting mass can be analysed before the normalization stage. In order to give more importance to newer ScanGrid , a discounting function is applied to the MapGrid before the fusion.

Based on this principle, several sensor models were proposed [START_REF] Yu | An evidential sensor model for velodyne scan grids[END_REF]]. Fig. 1 illustrates the concept of evidential grid. The left grid is an evidential occupancy grid where the green color shows the free cells (navigable), the red shows the occupied cells, while the blue represents conflicting cells and the black represents unexplored cells (unknownn). The color intensity reflects the certainty degree.The right grid is a binary grid computed from evidential one, with the value '0' for free cells and '1' for occupied cells. after the decision process. We consider that the state is occupied if f s (threshold) cells inside the state are occupied, otherwise it is considered as a free state. Instead of binary grid, we propose to use evidential grid where the mass is assigned to all subset of the domain which able this theory to represent uncertainty and conflict.

PLANNING WITH UNCERTAINTY

The local trajectory planning goal is the computation of an obstacle free local trajectory while following a desired global reference trajectory defined on a global map.

Trajectory planning with clothoid tentacles

Our planning approach is based on using a set of virtual antennas called tentacles in the egocentered reference frame related to the vehicle. Tentacles are a geometrical shape which models the dynamically feasible trajectories of the vehicle. Several forms of tentacles exist: circular tentacles [START_REF] Hundelshausen | Driving with tentacles: Integral structures for sensing and motion[END_REF]] and clothoid tentacles [START_REF] Himmelsbach | Autonomous O↵-Road Navigation for MuCAR-3[END_REF]; [START_REF] Chebly | A local trajectory planning and tracking for autonomous vehicle navigation using clothoid tentacles method[END_REF]]. In our work, we use clothoid tentacles because this method considers the current steering angle of the vehicle and make smooth variations in the vehicle dynamic variables such as the yaw rate, the sideslip angle and the steering angle.

Clothoid is a curve whose curvature varies linearly with curvilinear abscissa, also known as an Euler spiral, Cornu spiral or linarc. Its expression is presented by (Equ.3):

⇢ = 2 k 2 s ( 3
)
where ⇢ is the clothoid curvature, s is the curvilinear abscissa and k is a constant, representing the clothoid parameter.

For a fixed speed, all the tentacles begin at the center of gravity of the vehicle and take the shape of clothoid.

Tentacles of the extremity correspond respectively to the positive and negative maximal value (Equ. 4) of the reached steering angle which the vehicle can make at the current speed without losing stability.

⇢ max = a max V 2 x (4)
where a max is the maximum lateral acceleration. The length of tentacles increases with the increase of the speed. We assume that all tentacles generated for a given speed V

x have the same length. After generating all tentacles in the egocentred occupancy grid related to the vehicle, the next step is to choose the best tentacle to execute using di↵erent criteria.

Choosing the best tentacle

In order to choose the best tentacle to execute, we use the information provided by the occupancy grid. First we classify tentacles as navigable or not navigable. We define a security area as the distance over one second with the egovehicle speed. If a tentacle is obstacle free in this security area, we classify as a navigable one, otherwise it's not navigable (see Fig. 2).

Secondly, we need to choose from the navigable tentacles one to execute using di↵erent criteria. As it was presented in [START_REF] Mouhagir | A markov decision processbased approach for trajectory planning with clothoid tentacles[END_REF]], we modeled the decision problem as a MDP-like problem. We attribute reward regarding three criteria:

(1) Occupancy criterion: Since we need to judge every tentacle about its occupancy, we discretize each tentacle by using circles (their diameter represent the width of the vehicle with a margin of security) (Fig. 3). Then, we give positive reward to circles (states) free from obstacles, and negative reward for the occupied circles. (2) Trajectory criterion: To calculate the reward to be attributed to states with regard to their closeness to the global reference trajectory, defined for example by GPS waypoints and a global map, we calculate the lateral displacement between the tentacles and the reference trajectory at di↵erent points of the tentacle. These points are chosen in function of the crash distance. The crash distance l c is the distance needed to stop a vehicle traveling with a speed V

x , with a maximum longitudinal deceleration a m = 1.5 m/s 2 that maintains passenger comfort; it is calculated by Equation5 (where l s is a security margin)

l c = V 2 x 2a m + l s ( 5
)
(3) Overtaking criterion : In the case of the presence of an obstacle in front of the vehicle, the tentacles of the left receive an additional reward since the overtaking is done by the left.

For trajectory and overtaking criteria, we used the same reward as presented in [Mouhagir et al. 2016a]. Then the tentacle reward is:

R(tentacle) = ns X k=0 k t R(s k|trajectory ) + ns X k=0 k o R(s k|occupancy ) ns X k=0 k f R(s k|f ree ) + R(lef t) (6)
where t , o and f (Equ. 6) are discount factors that can be used to change the behavior of our approach, and that represent distance attenuation of each kind of reward. n s is the number of state per tentacle, s k is the state number k in the tentacle.

For occupancy criterion, we used binary grid with the value '0' for free cells and '1' for occupied cells. We consider that the state is occupied if f s (threshold) cells inside the state are occupied, otherwise it is considered as a free state. Instead of binary grid, we propose to use evidential grid where the mass is assigned to all subset of the domain which able this theory to represent uncertainty and conflict.

The states definition in our MDP-like model helps us to discretize the environment ahead the vehicle. To use information provided by the evidential grid, we superimpose the states on the grid (the state is a circle). This superimposing gives a matrix which contains several cells. Each cell contains 4 beliefs (Fig. 4).

We dispose of matrix englobing each state ( circles around the vehicle), each cell of the matrix provide mass about the occupancy.

In order to define a reward regarding the occupancy of the state, we propose to process cells information using four di↵erent rules. We consider that each cell is a source of information about the occupancy of the state. All cells are defined in the same frame of discernment.

• Conjunctive rule • Dempster's rule • Mean of the mass • Occupied and unknown cells number For each rule, we attribute a di↵erent reward (Equations 6 to 9, where a 1 , a 2 , a 3 , a 4 are weighting parameters see Table 1): (1) Conjunctive rule:

Reward occupation = a 1 m(F) + a 2 m(O) +a 3 m(⌦) + a 4 m( / O) (7)
The conjunctive rule is used if all sources of information are telling the truth. By applying this rule, we obtain a consensus between all sources of information.

(2) Dempster's rule:

Reward occupation = a 1 m(F )+a 2 m(O)+a 3 m(⌦) (8

SIMULATION RESULTS

To compare The use of evidential grid instead of the binary grid, we used an exemple of an evidential grid with a lot of uncertainty (Fig. 5). We generated a set of 41 tentacles on each grid. To compute the reward with an evidential grid we used the Conjunctive rule.

With the binary grid , the uncertain cells are considered as occupied. With an error detection as in Fig. 5, the algorithm will choose a tentacle of the right which don't include an obstacle because the left and middle tentacles passes by an uncertain cells (Fig. 6).

With the evidential grid, having an uncertainty represents an additional information that we choose to penalize but less then an obstacle. The algorithm don't try to avoid uncertain cells like occupied cells. In this case, the selected tentacle is the nearest to the reference trajectory even if it includes some uncertain cells.

System set-up

To validate the algorithm, we use SCANeR™Studio simulator to get data for simulation. The data was processed in Matlab. From this simulator data, we created a global map with a reference trajectory, the navigable space on black and the occupied one on white. We positioned two static obstacles (Fig. 7). The obstacles are represented by circles of diameter 2.5 m.

For each cell of the global map, we a↵ect 4 masses depending on its occupancy. If the cell with the coordinate (i, j) is on the navigable space, m

[i, j] = [m(F ) m(O) m(⌦) m(;)],
where m(F ) = rand(0.5, 1) (random number between 0.5 and 1), m(O) = 0, m(⌦) = 1 m(F ) and m(;) = 0. If the cell is on the occupied space; m(O) = rand(0.5, 1), m(F ) = 0, m(⌦) = 1 m(0) and m(;) = 0. We can see in Fig. 1, the right and left borders of the road and behind obstacles in the evidential grid represent a lot of uncertainties. In order to represent this uncertainty, if the cell is in the road borders or behind obstacles; m(⌦) = rand(0.5, 1), m(F ) = 1 m(⌦), m(O) = 0 and m(;) = 0. In every time step, we update the grid.

For each sampling time, we dispose of a local occupancy grid of 800⇤800 cells. The cell is represented by a square of 25cm. The state is represented by circles of diameter 2.5m. The matrix including the state is a matrix of 10 ⇤ 10, then we dispose of 100 cells as a source of information for each state. The table below contains the parameters of di↵erent combinaison rules.

Rule

a 1 a 2 a 3 a 4 Conjunctive 20 -20 -1 -50 Dempster 20 -50 -1 -Mean 10 -50 -1 -Cell-number 20 -50 -2 -Table 1. Parameters of di↵erent combination rules.

Results

In order to demonstrate the di↵erence between combination rules, we tested all di↵erent rules on the same scenario. We set the ego vehicle velocity to 10 m/s, we positioned the obstacles.

We tried at first the scenario with a binary grid, the egovehicle couldn't overtake the second obstacle, because the algorithm didn't find any navigable tentacles, in this case, it choses to brake.

The Fig. 8 shows the behavior of the ego-vehicle with different combination rules using an evidential grid. the main di↵erence between those several combination rules are time computing and the distance d between the obstacle and the vehicle after returning to the reference trajectory (see Fig. 8). Conjunctive and Dempster combination rule are not suitable for real-time application. The return to the reference trajectory take more time than the Mean and Cell-number Combination rules. The main advantage of the proposed algorithm is to planify a trajectory while taking into consideration the uncertainty of the environment. The use of evidential grid provide informatoion about the unknown which enable us to process it di↵erently from the occupied space.

CONCLUSION AND PERSPECTIVES

In this work, the goal is to integrate uncertainty of the environment in the planning trajectory using evidential grid. The simulation results show good performance of our algorithm in avoiding obstacles under uncertainty and underline the di↵erence between using an evidential grid instead of a binary grid . Among the perspectives, we aim to test the algorithm with more di↵erent scenarios and implement it in a robotized vehicle. We also aim to use a control approach to execute the selected tentacle.

  After the MapGrid processing, a cell contains a mass function [m(;) m(F ) m(O) m(⌦)]. The value of m(⌦) represents the uncertainty, m(;) the conflict resulting from a combination of free mass m(F ) and occupied mass m(O). A decision process can be applied to decide the state of the cell. To clarify the above definition, here we show some mass distributions as examples: [m(;) m(F ) m(O) m(⌦)] =[0 0 0.7 0.3] indicates an Occupied cell with 0.7 as a belief, the rest of the mass is in Unknown. [m(;) m(F ) m(O) m(⌦)] =[0 0.6 0 0.4] shows we have belief 0.6 in F ree state, the rest of mass are in Unknown.

Fig. 1 .

 1 Fig. 1. From evidential grid to binary grid. The blue rectangle represents the vehicle position.

Fig. 2 .

 2 Fig.2. The concept of classifying tentacles as undrivable only in case of being occupied within a speed-dependent crash distance (see main text). In this case, some drivable tentacles remain, allowing a pass of the car.

Fig. 3 .

 3 Fig. 3. Decomposing each tentacle into several circles.

Fig. 4 .

 4 Fig. 4. The superposition of the tentacles on the grid. Each tentacle is a set of circles.

  ) The normalization process in Dempster's rule has the e↵ect of distributing the belief from the conflict to the other propositions, according to their respective mass (3) Mean of the mass Reward occupation = a 1 mean m (F ) + a 2 mean m (O) +a 3 mean m (⌦) (9) (4) Cells number Reward occupation = a 1 Nb(F ) + a 2 Nb(O) + a 3 Nb(⌦) (10) with Nb(F ) for example refers to the number of free cells.

Fig. 5 .

 5 Fig. 5. An evidential grid created using a Lidar 4 nappes. The green color shows the free cells, the red shows the occupied cells and the black represents unexplored cells (unknownn). The yellow circle includes a error detection because of snow on the Lidar.

Fig. 6 .

 6 Fig.6. The left grid is an evidential grid, the selected tentacle is on pink. The right grid is a binary grid, the selected tentacle is on pink.

Fig. 7 .

 7 Fig. 7. Scenario test from SCANeR™Studio simulator. (a): the obstacles are represented by red circles. (b) This figure represents an evidential grid; the navigable space is in green, the occupied space in red and unknown in black.

Fig. 8 .

 8 Fig. 8. The behavior of the ego-vehicle using the evidential grid.

Table 2 .

 2 The computing time is calculated for a road of length 200 m Time computing and distance d for di↵erent combinaison rules.

	Rule	Conjunctive Dempster Mean Cell-number
	Time (s)	320	460	125	96
	d(m)	25	32	12	15


Edurne Redondo

Wan-Yu Tsai

Barbara Daffos

Pierre-Louis Taberna

Patrice Simon
email: simon@chimie.ups-tlse.fr

Eider Goikolea

Roman Mysyk
email: rmysyk@cicenergigune.com

Outstanding room-temperature capacitance of biomass-derived microporous carbons in ionic liquid electrolyte

A remarkable capacitance of 180 F•g -1 (at 5 mV•s -1 ) in solvent-free room-temperature ionic liquid electrolyte, 1-ethyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide, was achieved in symmetric supercapacitors using microporous carbons with a specific surface area of ca. 2000 m 2 •g -1 calculated from gas sorption by the 2D-NLDFT method. The efficient capacitive charge storage was ascribed to textural properties: unlike most activated carbons, high specific surface area was made accessible to the bulky ions of the ionic liquid electrolyte thanks to micropores (1-2 nm) enabled by fine-tuning chemical activation. From the industrial perspective, a high volumetric capacitance of ca. 80 F•cm -3 was reached in neat ionic liquid due to the absence of mesopores. The use of microporous carbons from biomass waste represents an important advantage for large-scale production of high energy density supercapacitors.

Introduction

Electrical double layer capacitors (EDLCs) store charge by electrostatic interaction between electrolyte ions and electrode surface charges [START_REF] Simon | Materials for electrochemical capacitors[END_REF]. Room temperature ionic liquids (RTILs) [START_REF] Ohno | Electrochemical Aspects of Ionic Liquids[END_REF] have been proposed as electrolytes for advanced and safe EDLCs for their wide stable electrochemical window, wide operational temperature range and non-volatility. However, RTILs exhibit high viscosity and low ionic conductivity at room temperature; hence, electrolyte ions have hindered access into the narrow micropores of commercial activated carbons (ACs). Thus, RTIL-based supercapacitors often show low capacitance and high resistance compared to those using conventional electrolytes, based on organic solvents (acetonitrile or propylene carbonate) [START_REF] Matic | Ionic liquids for energy applications[END_REF][START_REF] Mac-Farlane | Energy applications of ionic liquids[END_REF][START_REF] Mysyk | Capacitance evolution of electrochemical capacitors with tailored nanoporous electrodes in pure and dissolved ionic liquids[END_REF][START_REF] Handa | A neat ionic liquid electrolyte based on FSI anion for electric double layer capacitor[END_REF]. In this regard, two different approaches have been pursued to circumvent the drawbacks of RTILs and make them efficient in supercapacitors: i) dissolving RTILs in small amounts of organic solvents to increase ionic conductivity [START_REF] Brandt | An investigation about the use of mixtures of sulfonium-based ionic liquids and propylene carbonate as electrolytes for supercapacitors[END_REF], and ii) employing electrode materials with fully electrolyte-accessible (open) surface, such as exohedral carbons [START_REF] Lin | Capacitive energy storage from -50 to 100 °C using an ionic liquid electrolyte[END_REF] or mesoporous carbons [START_REF] Wei | Polypyrrole-derived activated carbons for high-performance electrical double-layer capacitors with ionic liquid electrolyte[END_REF]. The first approach is achieved detrimentally to the maximum cell voltage. The second cannot provide high capacitance (due to the low specific surface area (SSA) of such materials), and also requires complex synthetic procedures and/or expensive synthetic precursors. Recent investigations demonstrated improvements in gravimetric capacitance by combining RTILs containing 1-ethyl-3-methylimidazolium (EMI + ) ion and micro/mesoporous carbons with high pore volume (~2 cm 3 •g -1 ) [START_REF] Wang | Geometrically confined favourable ion packing for high gravimetric capacitance in carbon-ionic liquid supercapacitors[END_REF][START_REF] Lazzari | Mesoporous carbon design for ionic liquidbased, double-layer supercapacitors[END_REF]. However, high mesopore volume is detrimental to the density of materials. Thus, volumetric capacitance, the most industry-demanded metric, can be adversely affected with such carbons.

In this work, a series of ACs derived from low-cost green precursors (olive pits) was synthesized [START_REF] Redondo | Effect of pore texture on performance of activated carbon supercapacitor electrodes derived from olive pits[END_REF] and tested as electrode materials in neat 1-ethyl-3-methylimidazolium bis(trifluoromethanesulfonyl)imide (EMI-TFSI) at room temperature. These carbons contain only micropores that can be easily fine-tuned through synthesis parameters. The results showed high gravimetric and volumetric capacitance using such mesopore-free materials and EMI-TFSI within 3 V, thus offering interesting opportunities for industrial development since ACs come from cheap and abundant natural precursors.

Experimental

ACs were prepared by chemical KOH activation of olive pits, as reported elsewhere [START_REF] Redondo | Effect of pore texture on performance of activated carbon supercapacitor electrodes derived from olive pits[END_REF]13]. Briefly, the precursor was carbonized in a tubular furnace under an Ar flow of 100 mL•min -1 by heating at 5 °C•min -1 and dwelling for 2 h at 700 °C. The samples of carbon char were mixed with different amounts of KOH and heated up under the same conditions described in the first step. Last, the ACs were washed off with diluted HCl and water until neutral pH, and dried at 120 °C under vacuum overnight.

N 2 adsorption was conducted using an ASAP2460 instrument (Micromeritics). The samples were outgassed under vacuum at 250 °C for 24 h before analysis. N 2 isotherms were measured at 77 K for relative pressures (P/P 0 ) between 10 -7 and 0.995. The SSA and pore size distribution (PSD) were calculated using the SAIEUS software with 2D-NLDFT [START_REF] Jagiello | 2D-NLDFT adsorption models for carbon slit-shaped pores with surface energetical heterogeneity and geometrical corrugation[END_REF]. The differential pore volume (dV/dlgL) was calculated as:

dV d lg L = dV dL L ln 10 (1)
Average pore size was calculated as the weighted average from PSD, according to Eqs. ( 2) or (3):

∫ L = LdV (V -V ) 0 V V tot min min tot (2)
∫ L = LdV (V -V ) i V V tot is is tot (3)
where L 0 and L i correspond to the average pore size and the average ion-inaccessible pore size, L the pore size, V is the ion-inaccessible pore volume, and V tot the total pore volume from the cumulative DFT distribution [START_REF] Redondo | Effect of pore texture on performance of activated carbon supercapacitor electrodes derived from olive pits[END_REF]. The electrodes were made by mixing 95 wt% of ACs with 5 wt% of polytetrafluoroethylene (PTFE) binder from a 60 wt% aqueous dispersion. The mixture was stirred in ethanol to form a dough further rolled to a thickness of ~170 μm and dried under vacuum at 120 °C overnight. Disk electrodes of 11 mm diameter were cut out with the electrode mass between 7 and 8 mg•cm -2 . Two-electrode symmetric supercapacitors were assembled in Swagelok® cells using two identical activated carbon electrodes, a borosilicate glass fiber separator (Whatman GF/B) and EMI-TFSI, 99.9% (Solvionic) as electrolyte. Cell assembly was conducted in a glove box under Ar atmosphere with < 1 ppm of water and oxygen.

Electrochemical measurements were done at room temperature, 20 °C, using a multichannel potentiostat/galvanostat VMP3 (Biologic): cyclic voltammetry (CV) at a scan rate of 5 mV•s -1 , galvanostatic cycling (GC) at 0.1-30 A•g -1 •of active material per electrode and electrochemical impedance spectroscopy (EIS) from 1 MHz to 10 mHz.

Gravimetric and volumetric electrode capacitance (C) was calculated using Eqs. ( 4) and ( 5), respectively:

∫ C = 2• Idt (U•m) (4) ∫ C = 2• Idt (U•π•r •h) 2 ( 5
)
where I is the current, t the discharge time, U the voltage, m the active material mass per electrode, r the radius and h the electrode thickness.

Series resistance was evaluated from the intercept of the real axis at high frequency of the Nyquist plot, and in-pore ionic resistance from the intercept of quasi-vertical line at low frequency with the real axis after excluding the series resistance [START_REF] Taberna | Electrochemical characteristics and impedance spectroscopy studies of carbon-carbon supercapacitors[END_REF].

Results and discussion

Textural properties are shown in Fig. 1 and Table 1. Since the maximum capacitance of carbide-derived porous carbons was found at pore size of ~0.72 nm using neat EMI-TFSI [START_REF] Largeot | Relation between the ion size and pore size for an electric double-layer capacitor[END_REF], pores narrower than 0.70 nm are considered poorly accessible to electrolyte ions due to the ion-sieving effect. Ion-accessible pore volume and surface area calculated using this cut-off (> 0.70 nm), d 50 and d 90 are listed in Table 1. d 50 and d 90 are the pore widths corresponding to 50 and 90% of the total pore volume and their use was recently suggested for assessing PSD [START_REF] Jäckel | Increase in capacitance by subnanometer pores in carbon[END_REF]. All the ACs have pores in the micropore range (< 2 nm) and, as reported elsewhere [START_REF] Ahmadpour | The preparation of active carbons from coal by chemical and physical activation[END_REF], PSD is widened with the higher KOH/ carbon ratio. Thus, AC2 exhibits the smallest L 0 and d 50 among the studied ACs. Although AC3-AC6 have similar SSA, an increasing L 0 is observed from AC3 to AC6. Moreover, the difference between d 90 and d 50 increases correspondingly, meaning higher pore size dispersity with more KOH.

Fig. 2a andb show the CVs of symmetric cells for AC2-AC6 at 5 mV•s -1 in EMI-TFSI. Most of the samples exhibit rectangular CVs typical of supercapacitors. Most importantly, high specific capacitance of 179 F•g -1 , 163 F•g -1 and 171 F•g -1 was measured for AC4, AC5 and AC6, respectively. To our knowledge, such high capacitance values have never been reported for purely microporous carbons in neat RTILs. By contrast, AC2 shows very low gravimetric capacitance since d 90 is below 0.75 nm, thus poorly accessible to cations and anions, in agreement with the accessible SSA of only 292 m 2• g -1 (Table 1). Compared with AC2, AC3 shows decent gravimetric capacitance with huge distortion at high polarisation, meaning that, even with higher SSA, not all the pores are easily accessible to the electrolyte. The increase in d 50 beyond 0.70 nm and the associated L i , such as that achieved for AC4, enable a nice typical capacitive signature within 3 V. Thus, AC4 has a PSD wide enough to provide good access for EMI + and TFSI -ions to a large part of microporous surface, also achieving high gravimetric capacitance. Further increasing L i shows no improvement in capacitance (from AC4 to AC6). The higher capacitance of AC4 vs AC5 can arise due to stronger ion confinement due to narrower PSD as suggested theoretically [START_REF] Merlet | Highly confined ions store charge more efficiently in supercapacitors[END_REF] and experimentally measured [START_REF] Largeot | Relation between the ion size and pore size for an electric double-layer capacitor[END_REF][START_REF] Jäckel | Increase in capacitance by subnanometer pores in carbon[END_REF][START_REF] Chmiola | Anomalous increase in carbon capacitance at pore sizes less than 1 nanometer[END_REF].

More interestingly, Fig. 2b shows that a high volumetric capacitance of 80, 75 and 63 F•cm -3 was achieved for AC4, AC5 and AC6, respectively. Such high values in RTILs are unusual for biomass-derived microporous carbons with irregular porosity and are comparable or even higher than in solvent-based electrolytes [START_REF] Wei | Nanostructured activated carbons from natural precursors for electrical double layer capacitors[END_REF]. Since the volumetric capacitance is a key parameter from industrial prospective regarding device miniaturization, these results are highly promising for the energy density of devices. Obviously, high volumetric capacitance was achieved thanks to the moderate pore volume in strictly microporous carbons, which distinguishes them from carbons with ultrahigh-porе volume (~2 cm 3 •g -1 ) that also provide high gravimetric capacitance, but have significant mesoporosity, which is detrimental to volumetric performance [START_REF] Wei | Polypyrrole-derived activated carbons for high-performance electrical double-layer capacitors with ionic liquid electrolyte[END_REF]. A recent study [START_REF] Leyva-Garcia | Electrochemical performance of a superporous activated carbоn in ionic liquid-based electrolytes[END_REF] also reports high gravimetric capacitance in neat IL electrolyte for a carbon with ~20% higher pore volume than that of AC4, detrimentally to the volumetric capacitance (not calculated).

Rate capability is an important metric in supercapacitor perfor-mance, which depends on the complex interplay between textural and electrical properties of porous carbons and in-pore ion transport [START_REF] Chmiola | Anomalous increase in carbon capacitance at pore sizes less than 1 nanometer[END_REF][START_REF] Tamai | Highly mesoporous carbon electrodes for electric double-layer capacitors[END_REF]. Fig. 3 shows that capacitance retention is poor for AC2 and AC3, due to the poorly accessible porous structure. It increases for AC4-AC6 showing similar capacitance retention of ~65% at 5 A•g -1 and ~40% at 10 A•g -1 . The similar capacitance retention for AC4 to AC6 evidences that AC4 provides a well-suited PSD to ensure not only high capacitance, but also sufficiently fast ion transport in micropores.

No harsher activation conditions are required other than a KOH-carbon ratio of 4 at 700 °C. The observed capacitance loss can be linked to the limited ionic conductivity (8.4 mS•cm -1 ) and high viscosity (28.0 mPa•s) of EMI-TFSI [START_REF] Handa | A neat ionic liquid electrolyte based on FSI anion for electric double layer capacitor[END_REF]. For the conventional EDLC salt, TEABF 4 , conductivity reaches up to 60 mS•cm -1 in acetonitrile [START_REF] Devaraian | Novel ionic liquid electrolyte for electrochemical double layer capacitors[END_REF] and 20 mS•cm -1 in propylene carbonate [START_REF] Ue | Chemical capacitors and quaternary ammonium salts[END_REF].

Nyquist plots (Fig. 3b) show typical capacitive impedance response with a quasi-vertical line at the low frequency (except for AC2), and a ~45°slope line in the medium frequency due to the porous electrode RC distribution [START_REF] Hahn | Interfacial capacitance and electronic conductance of activated carbon double-layer electrodes[END_REF][START_REF] Portet | Modification of Al current collector surface by sol-gel deposit for carbon-carbon supercapacitor applications[END_REF]. Fig. 3b demonstrates a rather low series resistance, varying between 2.0 and 2.8 Ω•cm 2 for AC4-AC6 electrodes, whereas the in-pore ionic resistance fluctuates within 3.8-7.0 Ω•cm 2 . Volume (> 0.70 nm) (cm The last confirms that the porosity of AC4 is well adapted to provide efficient ion transport with EMI-TFSI, and further pore enlargement is not needed for high power demand. Both low series and in-pore resistance are comparable with the literature data for another ionic liquid with the same cation (EMI + BF 4 -) [START_REF] Wei | Polypyrrole-derived activated carbons for high-performance electrical double-layer capacitors with ionic liquid electrolyte[END_REF]. In that case, carbons with a significant mesopore volume favoured more rapid in-pore ion transport, detrimentally to volumetric capacitance. By contrast, our results are obtained with the ACs of a d 90 below 2 nm, thereby suggesting that mesoporosity is not always required to ensure fast propagation of RTIL ions inside pores. Overall, impedance data also evidence efficient high-rate operation with RTILs and the studied microporous carbons.

Conclusions

In summary, microporous carbons from olive pits deliver a high capacitance of 180 F•g -1 and a low resistance of 4 Ω•cm 2 at room temperature in neat EMI-TFSI ionic liquid. This work reveals efficient capacitive response with RTILs and strictly microporous carbons, which also enables a high volumetric capacitance of 80 F•cm -3 . Furthermore, carbons were prepared from biomass waste via a regular chemical activation procedure, which excludes complicated high-cost synthetic routes and synthetic precursors, and is therefore easily scalable.

Although the electrochemical behaviour showed good agreement with the ion-accessible area, it is still difficult to know the best carbon microstructure (PSD, relationship between ion-accessible SSA and volume …) due to the lack of techniques to probe carbon geometric topology, and in-situ ion transport. Apart from the accessibility of pores to ions, other parameters, including surface chemistry and defects [START_REF] Moussa | Relationship between the carbon nano-onions (CNOs) surface chemistry/defects and their capacitance in aqueous and organic electrolytes[END_REF], need to be thoroughly investigated to provide detailed insight into the outstanding performance of microporous carbons in RTILs.

Fig. 1 .

 1 Fig. 1. (a) N 2 adsorption/desorption isotherms (b) cumulative (c) differential pore volume (dV/dlgL) vs pore size calculated by the 2D-NLDFT model.

  nm) d 50 (nm) d 90 (nm) DFT-SSA (> 0.70 nm) (m 2 •g -1 )

Fig. 2 .

 2 Fig. 2. Cyclic voltammograms of ACs from olive pits at a scan rate of 5 mV•s -1 in neat EMI-TFSI at room temperature [20 °C] (a) gravimetric and (b) volumetric capacitance.

Fig. 3 .

 3 Fig. 3. (a) Capacitance of ACs in neat EMI-TFSI as a function of current density (insetgalvanostatic charge-discharge profile at 1 A•g -1 ); (b) Nyquist plot Ohm•cm 2 per electrode (inset -high frequency range).

Table 1

 1 Textural properties of the ACs.

  3

  •g -1 )

										L i (> 0.70 nm) (nm)
	AC2	2	1362	0.439	0.66	0.65	0.75	292	0.107	0.74
	AC3	3	2048	0.738	0.78	0.68	1.19	713	0.328	0.97
	AC4	4	1965	0.807	0.98	0.83	1.45	1031	0.523	1.14
	AC5	5	1986	0.858	1.01	0.91	1.55	1223	0.642	1.15
	AC6	6	2084	1.010	1.18	1.04	1.73	1486	0.844	1.30

Acknowledgments

This work was funded by the Basque Government under the Etortek Energigune '12 (Project Reference IE12-335) and Elkartek 2015 (Project CICE2015, Reference KK-2015/0000100) Programs. W.-Y. T. was supported by the European Research Council (ERC, Advanced Grant, ERC-2011-AdG, Project 291543-IONACES).


Giuseppina Todaro
email: giuseppina.todaro@etu.univ-tlse2.fr

Fabio Montermini
email: fabio.montermini@univ-tlse2.fr

Spatial reduplication in Sicilian: lexicon or grammar?

Introduction

In this paper we propose an analysis of a particular type of total NN reduplicative structures in Sicilian (and regional Italian spoken in Sicily) with a spatial semantic value. In particular, as we show, these constructions have the function of establishing a trajector / landmark spatial relation between two entities. As we will see, in different subtypes, the reduplicated noun can correspond either to the landmark or to the trajector. In the analysis we present these reduplications are considered as a morphological derivational (lexeme-forming) strategy, creating either adverbs or adjectives. In particular, we show that, in spite of the different input and output categories they specify, the homogeneity in the construction of their semantic interpretation justifies considering that all these strategies are indeed subtypes of the same, larger, construction. Moreover, we show that the semantic interpretation of Sicilian total reduplications crucially depend on the semantic features of the reduplicated noun, but also on the semantics of the related entity (typically expressed by a noun, but which can also be expressed by an explicit or implicit PRO) and of the verb marking the syntactic relation between the two. Consequently, we propose to consider that the morphological construction involving the reduplication is in turn encompassed into a larger construction which also includes en element (typically a noun) corresponding to the entity which is in a spatial relationship with the reduplicated noun. More globally, we consider that the data presented and the analysis proposed provide evidence in favor of considering reduplication as a particular subtype of compounding. Like compounding, it is useful to distinguish between cases in which reduplicated structures are the result of a general, cross-linguistic (and possibly universal) human ability to combine words and cases in which they correspond to grammaticalized lexeme-formation strategies submitted to language-specific constraints.

Our paper is organized as follows: in Section 2 we argue in favor of a joint analysis for compounding and (total) reduplication, and of identifying a dichotomy between two types of compounding / reduplication; Section 3 presents the data our treatment is based on; Section 4 proposes an analysis of Sicilian total reduplications in a Construction Morphology framework; finally, Section 5 contains some concluding remarks.

The place of reduplication in linguistic competence

Total reduplication (TR) can be considered as a particular type of compounding (cf. [START_REF] Bauer | Introducing linguistic morphology[END_REF]. Generally speaking, compounding consists in creating a lexeme by combining two (rarely more than two) other lexemes. Formally, in most cases the output lexeme results from the juxtaposition of the stems of the two input lexemes (although more complex cases are possible, cf. [START_REF] Montermini | Units in compounding[END_REF]. Semantically, the meaning of the output lexeme results from a function applied to the meanings of the two input lexemes (Guevara & Scalise 2009: 104). A rule of TR specifies that the two input lexemes are the same; consequently, the form of the output lexeme consists in the repetition of the stem of the input, and its meaning consists in a function applied to the meaning of the input (often involving such features as plurality, iterativity, intensification, etc.).

Compounding itself, however, can be seen as a complex and heterogeneous phenomenon. What we normally call "compounding", in fact, may correspond to at least two linguistic phenomena differing both in their origin and in their properties. On the one side, the presence of compound words in a language can be the outcome of a general cognitive ability to connect semantically two words by simply juxtaposing them. We propose to call this phenomenon Compounding1 (C 1 ). In this case, the juxtaposition of lexemes that takes place is closer to what happens in syntax, and, semantically speaking, the compound has a compositional meaning inferable from the sum of the meanings of the lexemes involved. When linguists cite compounding as the "widest-spread morphological technique" (Dressler 2006: 23), it is probably C 1 that they have in mind. On the other side, the rules for forming compound words differ significantly from one language to another and are submitted to various kinds of restrictions and constraints, which include phonological and prosodic constraints on the form of the input stems, constraints on the semantic compatibility between the two lexemes involved, constraints on head placement, constraints on the presence of "linking elements", which can be obligatory (e.g. -o-, or sometimes a different vowel, in Modern Greek, cf. Ralli 2013) or optional (e.g. -e-, -en-, -s-in German and Dutch, cf. [START_REF] Libben | Interfixation in German compounds: What factors govern acceptability judgements?[END_REF]Don 2009: 380-381, respectively). These facts suggests that, in another sense, compounding, like all other derivational phenomena, consists in a set of morphological patterns that are codified in the grammar of individual languages, and are therefore subject to different language specific parameters (cf. [START_REF] Bauer | Typology in compounds[END_REF][START_REF] Guevara | Searching for universals in compounding[END_REF][START_REF] Arcodia | Are reduced compounds compounds? Morphological and prosodic properties of reduced compounds[END_REF]. We propose to call this phenomenon Compounding2 (C 2 ).

Similar considerations can be applied to TR. In particular, a parallel distinction between Reduplication1 (R1) and Reduplication2 (R2) can be drawn. Cross-linguistically (and sometimes within the same language), we observe a sort of continuum going from R 1 , the repetition of the same word-form -usually for stylistic purposes -, to clear instances of R 2 , i.e. forms that represent the output of a language-specific process. [START_REF] Gil | From repetition to reduplication in Riau Indonesian[END_REF] argues in favor of a continuum ranging from stylistically marked repetition to strictly grammaticalized reduplication with a large greyish in-between area for which the classification is not straightforward. We can consider that R 1 stands between the two poles identified by Gil, as we show in (1):

(1) ‹- ---------------------------------------------› repetition R 1 R 2

Repetition (or reiteration) is a pragmatic cross-linguistic device generally employed in oral speech (less often in writing) to mark emphasis. Unlike in typical reduplication, the resulting structures are not necessarily binary, as units can be repeated recursively (2a); moreover, the units involved are not necessarily stems or word forms, but may consist in larger syntactic units, such as APs (2b); and finally, the repeated units are not necessarily contiguous, since other units, such as conjunctions, can be intercalated between them (2c):

(2) a. He runs, runs, runs and climbs everything like a little monkey.

[http://haberdasheryfun.com/page/15] b. This is a very beautiful, very beautiful, sturdy table.

[http://www.wayfair.com/Abbyson-Living-Sienna-Dining- In its turn, R 1 has often a specific semantic function: it is restricted to the designation of a 'real' or prototypical instance of the object designated by the input lexeme. This phenomenon, largely described in the literature, has been observed in the colloquial speech of many languages and is often called Contrastive Focus Reduplication [START_REF] Ghomeshi | Contrastive focus reduplication in English (the salad-salad paper)[END_REF][START_REF] Forza | Doubling as a sign of morphology: A typological perspective[END_REF]).

In oral speech, one of the elements is often pronounced with a special intonation, marking emphasis (a fact we indicate with capital letters in (3)).

(3) a. I'll make the tuna salad, and you make the SALAD-salad b. Is he French or FRENCH-French? [Ghomeshi 2004: 308] Like C 1 , R 1 may be considered as a general feature of the human linguistic ability, whereas R 2 is a more specific phenomenon, submitted to language-specific parameters.

Both types of reduplication are attested in Sicilian: R1 constructions (4a) express one of the semantic values prototypically associated with reduplication with no specific grammatical feature (the same phenomenon can be observed in Italian, among others, cf. [START_REF] Wierzbicka | Italian reduplication: Cross cultural pragmatics and illocutionary semantics[END_REF][START_REF] Dressler | Morphopragmatics: Diminutives and intensifiers in Italian, German, and other languages[END_REF][START_REF] Forza | Doubling as a sign of morphology: A typological perspective[END_REF]); R 2 (4b), on the other hand, corresponds to a morphological lexeme-formation process: (4a) is an example of R1: here, no specific effect on the grammatical features of the input lexeme is observed (nìuri nìuri functions as an adjective like nìuri), and semantically it has the contrastive function referred to above. On the other side, (4b) is an example of R2. Here, the effect observed corresponds to what happens with typical derivational, lexeme-forming, phenomena: it has an effect on category (muru muru functions as an adverb, while muru is a noun), and a specific meaning, non-recoverable from the meaning of the input lexeme (cf. *camina muru) or from the meanings usually attributed to reduplication. Specifically, the reduplicated form in (4b) expresses the same spatial relationship expressed in English by the preposition along. R2 constructions like the one in (4b) constitute the main focus of this article.

The data

The analysis we present is based on a dataset collected from dictionaries, novels and essays, as well as from the scholarly literature on Sicilian. Moreover, some of the data have been collected from occasional exchanges with speakers from the Western area of Sicily (provinces of Trapani and Palermo). Sicilian exhibits the kind of asyndetic total R 2 (cf. [START_REF] Stolz | Total reduplication: syndetic vs. asyndetic patterns in Europe[END_REF] exemplified above in all its varieties, including in non-standard regional varieties of Italian. The phenomenon involves both nouns and verbs as inputs [START_REF] Caracausi | Ancora sul tipo 'camminare riva riva[END_REF][START_REF] Leone | Profilo di sintassi siciliana[END_REF][START_REF] Sgarioto | Caminari riva riva': su un fenomeno di reduplicazione nominale in siciliano[END_REF][START_REF] Amenta | La reduplicazione sintattica in siciliano[END_REF][START_REF] Emmi | La formazione delle parole nel siciliano[END_REF]. In this paper we focus on a particular kind of total NN reduplications that produce adjective-or adverb-like units. The constructions in question do not express any of the meanings generally attributed to reduplications (plurality, emphasis, intensity, iterativity, etc.); in fact, their function is to establish a spatial relationship between a trajector and a landmark, under specific semantic conditions (cf. [START_REF] Todaro | Internal localisation NN adv reduplication in Sicilian[END_REF] for a detailed semantic account).

The literature on reduplication generally considers TR as a potentially universal phenomenon [START_REF] Moravcsik | Reduplicative constructions[END_REF][START_REF] Stolz | Total reduplication: syndetic vs. asyndetic patterns in Europe[END_REF]. In its turn, reduplication as a proper morphological process (R 2 ) is often considered to be rare in Romance (and even in Indo-European) languages, although recent studies claimed that TR is not completely absent in these languages. With the help of statistic analyses, it has been shown, for instance, that reduplicated constructions are attested in the Romance languages spoken in the Mediterranean area (see [START_REF] Stolz | Total reduplication: the areal linguistics of a potential universal[END_REF]. These data, like the ones we consider, provide evidence in favor of considering "TR as a potential areal feature in the area of the putative Mediterranean Sprachbund" (Stolz et al. 2011: 519). Consequently, we consider R 2 as being part of the basic morphology of Sicilian. In particular, in Sicilian four types of lexeme-forming constructions involving reduplication can be identified: 1

(5) 2 a. [VV] N curri-curri run-run 'stampede' Po' si sintì na gran vociata e ci fu, nella parti opposta della pista, un movimento di curri curri. 'Then we heard a loud scream and a stampede movement was on the opposite side of the track' In this work we deal exclusively with types (5c) and (5d), i.e. with denominal reduplications forming adjectives and adverbs and expressing a spatial relation. In particular, we consider that in Sicilian three types of constructions are available in order to express a spatial relation between two entities: one of the entities is denoted by the input noun of the reduplicated construction, the other is denoted by a syntactically connected unit (in the unmarked case a NP).

Type A (6a') Type B (6a'') Type C (6b) In two of the types, the reduplicated unit can be either a singular (type A) or a plural (type B) nominal form. The output of the reduplication is an adverb. In type C the reduplicated unit can only be a plural nominal form, and the output functions as an adjective. Semantically, all three constructions denote the relative spatial localization of two entities.

[N SG N SG ] Adv [N PL N PL ] Adv [N PL N PL ] A

The analysis

Sicilian reduplications as constructions

For the analysis of Sicilian NN R 2 constructions we adopt a Construction Morphology approach (cf. [START_REF] Booij | Construction Morphology[END_REF]. Therefore, we claim that, like constructions, the reduplications in question instantiate generalizations made by speakers on sets of existing com plex words with a systematic correlation between form and meaning. In particular, we propose to represent the TRs exemplified in (6) as constructional schemas ([XX] α ) which, in their turn, are encompassed into larger constructions involving a semantically and syntactically related entity (in most cases expressed by a NP), that we represent as follows: [Y ℜ [XX] α ]. Although both levels can be characterized as constructions, the lowest level ([XX] α ) constitutes a typical morphological object, whereas the highest one ([Y ℜ [XX] α ]) corresponds to a typical syntactic object. However, as we will see below, both the lowest and the highest level display holistic semantic properties that cannot be accounted for simply on a compositional basis. If the reduplicated structure is an adjective (type C), Y corresponds to its head noun or to the NP it predicates; if the reduplicated structure is an adverb (types A-B), Y corresponds to a syntactically linked NP (see 6a', 6a'').

Sicilian R 2 constructions display some typical properties of morphological derivational processes: i) they have developed a range of specific meanings not recoverable from the combination of the meanings of the base lexemes; ii) their outputs correspond to typical lexical units (no insertion possible between the nouns, single primary stress, no recursivity); iii) they have an effect on the category of the lexemes they apply to, since they change a noun into an adverb or into an adjective.

From a semantic point of view, Sicilian R 2 constructions mark a spatial localization between a landmark (an anchoring entity) and a trajector (an entity to be located) (cf. Langacker 1987)3 . In types A-B, the reduplicated noun designates the landmark and the syntactically connected noun designates the trajector; in type C the situation is reverted: the reduplicated noun designates the trajector and the head noun of the NP in which the reduplication appears designates the landmark. In most cases, the landmark corresponds to a circumscribed entity with discrete boundaries, and the trajector is located within these borders. Virtually any object possessing a physical extension can function as a landmark within which a trajector can be located. Moreover, as we will show in the following sections, the semantic interpretation of the larger construction can be affected by some semantic features of the nouns involved, either as trajectors or as landmarks.

As we observed above, the construction we have globally characterized as ([XX] α ) corresponds, in fact, to three different constructions, each one with different specifications for some of their elements, which in are encompassed into the larger construction [Y ℜ [XX] α ]. The general construction and its sub-constructions are given in Figure 1. Spatial relations between the trajector and the landmark are generically indicated as IN, although they can correspond to different spatial configurations and distributions, which depend on the semantic type of each of the nouns involved.

Semantic constraints on the trajector

The global semantic interpretation of the constructions in question is conditioned by the semantic features of the participants involved. In this section, we focus on the constraints to which the trajector is submitted, whereas in the following sections we will consider the constraints on the landmark and on the verb involved in the construction.

In Types A and B, the trajector can correspond to a mobile entity moving within the boundaries of the landmark. These cases correspond to instances in which the trajector is animate. Here, the relationship between the landmark and the trajector is dynamic and involves a change of location of the trajector within the circumscribed space of the landmark. The trajector does not move in a linear way, going from one point to another, but rather randomly, occupying different points in an unordered way. On the contrary, if the trajector is inanimate the spatial relationship is necessarily static. In this case, it occupies a fixed position within the boundaries of the landmark, and the whole construction can be interpreted in three different ways. The choice of one of the interpretations crucially depends on the semantic properties of the nouns involved, as well as on pragmatic factors. ( 8 8a) is more likely interpreted as expressing a vague localization. In this case, the speaker only knows that the house in question has been built in the mountains, but ignores its exact localization. (8b) is more likely to be interpreted as expressing an incongruous localization.

Here, the plant is seen as occupying an unusual, possibly disturbing, place. In these two cases, the choice between the two interpretations pragmatically depends on the referent of the reduplicated noun: it is unlikely that someone cannot precisely locate an object within the limited space of a staircase. On the other side, it is absolutely plausible that someone does not know the exact location of a house in the mountains. Finally, (8c) is more likely interpreted as expressing a homogeneous distribution of the referent of Y within the circumscribed space of X. Note that this interpretation can be activated either when Y corresponds to a mass noun (like rina), or when it corresponds to a plural noun: Although pragmatics is clearly the main reason for distinguishing the semantic nuances observed in examples (8a-c), a common, underspecified, reading can be observed. In fact, in each of these cases, the relevant semantic factor is that the whole surface of the landmark is (at least potentially) involved in the spatial relation. The simplest case is represented by (8c) and ( 9): here Y (a rina, i ciura) occupies the totality of X's (casa) surface. On the other hand, in (8a-b) Y (a casa, sta pianta) may potentially occupy any point in X's (muntagni, scala) surface, and the exact point it occupies does not change the whole reading: in the case of (8a) it is irrelevant; in the case of (8b), whatever point occupied by Y constitutes an incongrous location.

By contrast with types A and B, in type C the reduplicated noun corresponds to the trajector. In this case, the input of the reduplication is necessarily a plural noun form. The semantic interpretation is similar to that of (8c): here the trajector is interpreted as being homogeneously distributed within the landmark's boundaries. As it can be seen the value [+PL] is directly encoded in the construction of this type of reduplications. In this case, X (the reduplicated noun) can be either animate or inanimate, without any change in meaning, as the examples (10a-b) below show. As we observed above, such structures are not acceptable if X corresponds to a singular noun (10c); they are also unacceptable if Y is [-count] (10d). ( 10

Constraints on V

As the representation in Figure 1 shows, the TRs under discussion enter in a larger construction whose function is to relate two entities, one of which is designated by the input noun of the reduplication. The related entity can be designated either by an explicit NP or by a PRO-form. Since Sicilian is a PRO-drop language, the latter may not be explicit (cf. ( 10)). In types A and B, it usually corresponds to one of the arguments of a verb which is modified by the adverbial reduplicated structure. In type C, it mostly corresponds to a NP modified or predicated by the adjectival reduplicated structure. Types A and B do not display any specific restriction on the types of verbs involved. As we observed above, in fact, in different subtypes the spatial relation between the trajector and the landmark may be either static or dynamic, thus making both dynamic and stative verbs acceptable. Several different readings are available for the same construction and are not necessarily mutually exclusive. Moreover, we claim that, if the trajector is [+animate], a dynamic meaning is intrinsic in the construction itself. This seems to be confirmed by the fact that, in this case, even a neuter verb like essiri 'be' entails a dynamic reading, like in ( 11):

(11) U picciriddru è casa-casa In this case, the reduplication has the same function and the same distribution of a qualifying adjective.

Constraints on the landmark

In type C, there are no specific constraints on the entity that can correspond to the landmark. In fact, as in all the other types of reduplications considered, the only condition is that the landmark corresponds to a physical entity which can delimit a mono-(13a) or a multidimensional (15b) space with discrete boundaries. The trajectors (i.e., in this case, several instances of the entity designated by the reduplicated noun) are homogeneously distributed on the surface in question. As far as type A is concerned, on the other hand, the meaning of the entire construction can be slightly modified by some of the features of the landmark, as Figure 1 shows.

If the landmark corresponds to an entity which can be viewed as a mono-dimensional space (along which only a monodirectional movement or distribution is possible), the reduplication is likely to mark a carrier relationship, similar to that expressed by the English prepositions along or on. In this case, the reading of the construction containing the adverb arvuli-arvuli implies a multiple and dynamic localization of the trajector (the grandfather) within the landmark; in its turn, the landmark corresponds to an area containing trees and surrounded by an imaginary outline (cf. [START_REF] Herskovits | Language and spatial cognition[END_REF]. Of course, the landmark may also correspond to a space with real boundaries. In this case, the plural indicates a movement taking place successively in several of these spaces, like in (19). The connection between reduplication and iconicity is often pointed out in the literature, since cross-linguistically these constructions often express plurality, intensity, emphasis, iterativity, etc. Roughly speaking, some of these meanings (e.g. plurality or iterativity) can also be attributed to the Sicilian reduplications we presented in this paper. However, we showed that the range of meanings these reduplications may express are restricted and crucially determined by the syntactic context, the semantics of the elements involved, etc., i.e. by the construction which is responsible for their formation. This observation led us to consider reduplication as a phenomenon proper to the human speech ability which can eventually grammaticalize and give birth to constructions, such as the ones we presented, which are formally and semantically constrained. This grammaticalization process can result in a derivational phenomenon (like the one we investigated here) or an inflectional one (like for instance, in plurals expressed by reduplication in various languages). What we claimed is that TR can be considered a special type of compounding and that, like for compounding (cf. [START_REF] Bauer | Typology in compounds[END_REF][START_REF] Arcodia | Are reduced compounds compounds? Morphological and prosodic properties of reduced compounds[END_REF], it is possible to draw a distinction between two kinds of reduplication: R 1 , which is the manifestation of the (potentially universal) ability of humans to reduplicate a linguistic object (e.g. a word) in a fairly iconic way (cf. (2) above) and R 2 , which corresponds to a phenomenon codified in the grammar of individual languages under the form of a construction for which formal, categorial and semantic constraints are specified.

  SG.PRES.IND DET.M.PL eye.M.PL black.M.PL black.M.PL 'He/she has really black eyes' b. (R 2 ) Camina muru muru walk.3.SG.PRES.IND wall.M.SG wall.M.SG 'He/she walks along the wall'

  [A. Camilleri, La pista di sabbia. Palermo: Sellerio Editore] b. [VV] A cala-cala go down-go down [A. Camilleri, La rivoluzione della luna. Palermo: Sellerio Editore]

Figure 1 :

 1 Figure 1: Types and subtypes of reduplicative spatial constructions in Sicilian.

  DET.M.SG boy.M.SG run.3.SG.IMPF.IND village.M.SG-village.M.SG 'The boy was running all over the village'

  have.1.PL.PRES.IND DET.M.PL flower.M.PL house.F.SG-house.F.SG 'We have flowers all over the house'

  DET.M.SG rope.F.SG be.3.SG.PRES.IND knot.M.PL-knot.M.PL 'The rope is full of knots' b. A facci è mpuddri-mpuddri DET.M.SG face.F.SG be.3.SG.PRES.IND pimple.F.PL-pimple.F.PL 'The face is pimply'

  DET.M.PL doctor.M.PL go around.3.SG.PRES.IND house.F.PL-house.F.PL 'The doctor goes from an house to another' 5. C o n c l u d i n g r e ma r k s

Table -

 -

	c. In fact, the tension builds so intensely as Lola runs, runs, and runs that we can
	only be thankful that the film has a relatively short running time.
	[http://www.hccentral.com/cgi-bin/films.cgi?fid=12]
	AD-DT-018-
	BYV2437.html]

Table 1 :

 1 Three types of NN total reduplications in Sicilian. DET.M.SG child.M.SG play.3.SG.PRES.IND house.F.SG-house.F.SG 'The child plays all over the house' a''. U cane camina muntagni-muntagni DET.M.SG dog.M.SG walk.3.SG.PRES.IND mountain.F.PL-mountain.F.PL 'The dog walks in/through the mountains'

	(6) a'. U	picciriddro ioca	casa-casa
	b. A	cammisa è	pirtusa-pirtusa

DET.F.SG shirt.F.SG be.3.SG.PRES.IND hole.M.PL-hole.M.PL 'The shirt is full of holes'

  make.3.SG.PST.IND DET.F.SG house.F.SG mountain.F.PL-montain.F.PL 'He/she built his/her house somewhere in the mountains' b. what there.CL do.3.SG.PRES.IND DEM.F.SG plant.F.SG stair.F.SG-stair.F.SG 'Why is that plant in the middle of the staircase (in the way)? PL.PRES.IND DET.F.SG sand.F.SG house.F.SG-house.F.SG 'We have sand all over the house'

	) a. Si	fici	a	casa	muntagni-muntagni
	Chi ci	fa	sta	pianta	scala-scala?
	c. Avemu	a	rina	casa-casa
	have.1.(

REFL

Table 1 :

 1 PL.PRES.IND oil.M.SG-oil.M.SGIn Table2, we sum up the syntactico-semantic constraints on the trajector we observed for types A, B and C, respectively. Syntactico-semantic constraints on the trajector in Sicilian reduplications.

		) a. Sugnu	puci-puci
		be.1.PL.PRES.IND flea.F.PL-flea.F.PL
		'I am full of fleas'
		b. Sugnu	papuli-papuli
		be.1.PL.PRES.IND blister.F.PL-blister.F.PL
		'I am full of blisters'
		*Sugnu	papula-papula
		be.1.PL.PRES.IND blister.F.SG-blister.F.SG
		d. *Sugnu	ogghiu-ogghiu
		be.1.[animate]	[count]	[±PL]
	A-B	+ (dynamic) / -(static)	+ (hom. distribution) / -(incongruity)	+ / -
	C	+ / -	+	+

  On the other side, a genuinely stative verb, in the same context, makes the sentence odd:

	DET.M.SG	child.M.SG	be.3.SG.PRES.IND	house.F.SG-house.F.SG
	'The child is (moving) all over the house'
	(12) 4 *U	picciriddru rorme		casa-casa
	DET.M.SG	child.M.SG	be.3.SG.PRES.IND	house.F.SG-house.F.SG
	'The child is sleeping all over the house'
	As far as type C is concerned, when it corresponds to a predicative structure, the verb is
	necessarily stative or psychological:
	(13) a. Sta	strata	è		curvi-curvi
	DEM.F.SG street.F.SG be.3.SG.PRES.IND turn.F.PL-turn.F.PL
	'That road is winding' (lit. full of turns)
	b. Mi	sentu		spinguli-spinguli
	REFL.1.SG feel.1.SG.PRES.IND	pin.F.PL-pin.F.PL
	'I fell very thrilled' (lit. I feel pins all over)

  IMPER=OBJ.F.SG river.M.SG-river.M.SG CONJ arrive.2.SG.PRET.IND 'Follow the river (lit. do it along the river) and you'll get there' Note that a structure as the one in example (15) corresponds to the only way available in Sicilian to express a spatial relation which in other Indo-European languages is usually expressed by a preposition (Eng.: along, It: lungo, etc.). Apart from spaces which are conceived as mono-dimensional, any space is usually interpreted as having different dimensions (at least two, like a sheet of paper or a table) whereon different movements or distributions are possible (along one of the three dimensions). If the landmark is multidimensional, then the movement (in the case of an animate trajector) or the distribution (in the case of a mass or a plural trajector) are seen as involving any dimension: PL.IMPF.IND walk.INF because there be.3.PL.IMPF.IND many petre strata-strata stone.F.PL street.F.SG-street.F.SG 'We couldn't walk because there were a lot of stones on the street'In standard Italian the same semantic nuance, differentiating between a simple localization and a dynamic localization, is expressed, respectively, by the prepositions a/in and per: DET.M.PL grandfather.M.PL stroll.3.SG.IMPF.IND tree.M.PL-tree.M.PL 'Grandfather was strolling among the trees'

	do.2.(16) a. I	picciotti iocano	a	palluni	strata-strata
	DET.M.PL boy.M.PL play.3.PL.PRES.IND PREP ball.M.SG street.F.SG-street.F.SG
	'Boys are playing football on the street'
	b. Un putìamu	caminari picchì	c'	eranu	assai
	NEG can.1.(17) a. I bambini	sono	a/in casa
	DET.M.PL children.M.PL be.3.PL.PRES.IND PREP house.F.SG
	'The children are in the house'
	b. I	bambini	sono	per casa
	DET.M.PL children.M.PL be.3.PL.PRES.IND PREP house.F.SG
	'The children are (moving) all over the house'
	Concerning type B, as already observed, the landmark can correspond to a plural noun form:
	(18) U	nonnu	passiava			arvuli-arvuli
	(15) Fattìlla		ciumi-ciumi	e		arrivasti

'which goes down easily' / 'easy-to-drink' Un vino fatto come lo facevano i nostri nonni, in poche parole un vino cala cala che ti inchiumma a tradimento ma con soddisfazione. 'A wine made like our ancestors used to make it, in short, an easy-to-drink wine which pins you down unexpectedly but with pleasure' [http://www.firriotate.com/2013/12/10/degustazione-vino-veritas/] c. [N SG N SG ] Adv casa-casa house-house 'all over the house' Noi picciriddri giocavamo a nascondino casa casa. 'We the children used to play to hide-and-seek all over the house' [http://ricerca.repubblica.it/repubblica/archivio/repubblica/2011/02/06/il-bonificodi-berlusconi-mia-nonna-maria.html] d. [N PL N PL ] A pirtusa-pirtusa holes-holes 'full of holes' Genti coi vistiti pirtusa pirtusa che cadivano a pezzi. 'People with very ripped clothes, falling apart' 1 For each type we provide real examples with an indication of the source. All the examples have been translated by the authors. 2 Forms like (5a) recall the Italian reduplications that produce nouns from verbs (fuggifuggi 'stampede', lit. run away-run away, cf.[START_REF] Masini | Italian VeV lexical constructions[END_REF], although in Italian the reduplication in question does not seem to be productive anymore.

The terms landmark and trajector correspond to the notions denoted as ground and figure respectively, e.g. by[START_REF] Talmy | How language structures space[END_REF].

The sentence in (12) is only acceptable in a context in which (i) the position of the child is considered as incongruous, (something like 'in the middle of the house', in contrast to 'in his bed'), (ii) a child is sleeping somewhere in the house, then he moves and he sleeps somewhere else, then he moves once again and he's still sleeping, and so on.


Amedeo Anselmi

Sophie Collin

Pascal Haigron

Jean-Philippe Verhoye

Erwan Flecher

Device-specific evaluation of intraventricular left ventricular

come

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