Guy Royer

G Ramasamy

Philippe Eudes

Energy of molecular structures in 12 C, 16 O, 20 Ne, 24 Mg and 32 S

Keywords: numbers: 21.60.Gx, 26.20.Fj, 25.60.Pj, 23.60.+e, 25.55.-e

HAL is

I. INTRODUCTION

α particles play a main role in the nucleosynthesis of 12 C, 16 O, and heavier elements and α-particle models have been developed [1][2][3][4]. The cluster-type states coexist with the mean-field-type states in these 4n-nuclei [START_REF] Horiuchi | Cluster in Nuclei[END_REF]6].

Theoretically, in 12 C the ground state wave function contains a large amount of 3α cluster wave function. In 16 O some excited states are due to the mean-field-type excitation mode while other ones are dominantly of the cluster structure of α+ 12 C [START_REF] Horiuchi | Cluster in Nuclei[END_REF]. For 16 O, recent ab initio lattice calculations using effective field theory lead for the ground state to a tetrahedral configuration of α clusters and for the first excited spin-0 state and first spin-2 state to a square configuration, in good agreement with the empirical energy spectrum and with the electromagnetic properties and transition rates [7]. Within an algebraic cluster model, a comparison with the experimental values of the energy of the low-lying spectrum and electromagnetic transitions have also provided strong evidence for tetrahedral symmetry in 16 O [8]. Using a Skyrme cranked Hartree-Fock method the existence in 16 O of a region of angular momentum (13)(14)(15)(16)(17)(18) where the linear chain configuration is stabilized has been demonstrated [9]. It has also been shown [10] that the highly fragmentation into several peaks of the giant dipole resonance spectrum of 12 C and 16 O is due to the different α structures of these nuclei. In connection with the excited 0 + 2 Hoyle state of 12 C (E * = 7.65 MeV) and possible excited Hoyle state of 16 O, (0 + 6 , E * = 15.1 MeV) the α condensate character of the α-linear-chain has been proposed after comparing a large number of Brink functions with Tohsaki-Horiuchi-Schuck-Röpke wave functions [11,12]. In 20 Ne the ground band states contain the α+ 16 O component at most 70% [START_REF] Horiuchi | Cluster in Nuclei[END_REF]. Within a three-dimensional cranked Skyrme Hartree-Fock method a stable state in 40 Ca with a torus configuration has been obtained at 60 and with an excitation energy of about 170 MeV [13].

Experimentally, in 12 C, a new high spin 5 -state at 22.4 MeV has been measured recently [14]. It fits very well the ground state rotational band of an oblate equilateral triangular spinning top with a D 3h symmetry characterized by the sequence 0 + , 2 + , 3 -, 4 + -, 5 -. For the 0 + 2 excited Hoyle state of 12 C an upper limit of 0.2% on the direct 3α decay has been obtained [15]. For the excited rotational band of 16 O, α+ 12 C resonant cluster structure has also been observed [16] as well as 4α-linear-chain [17,18]. In the nucleus 24 Mg in the range of 14-16 analysis of experimental data suggests that extremely prolate linear α-chains are populated [19]. Possible signatures of α clustering in light nuclei from relativistic collisions have been suggested [20]. α-208 Pb structure has also been observed in 212 Po [21].

In a previous work [22] the L-dependent energies and potential barriers governing the evolution of the 8 Be↔ 4 He+ 4 He, 12 C↔ 8 Be+ 4 He systems and the 12 C↔ 4 He+ 4 He+ 4 He oblate triangular and prolate longitudinal configurations have been determined in the framework of a Generalized Liquid Drop Model (GLDM) and of binary and ternary quasimolecular shapes. The purpose of the present work is to apply the same approach to study the 12 C, 16 O, 20 Ne, 24 Mg and 32 S 4n-nuclei assuming different planar and three-dimensional α-molecules : linear chain, triangle, square, tetrahedron, pentagon, trigonal bipyramid, square pyramid, hexagon, octahedron, octogon and cube (see Fig. 1). Within the α cluster model approach this study considers separated α particles starting from their contact point since it is extremely difficult mathematically to describe the strongly deformed one-body shapes appearing just before the birth of several α particles and the transition from one quasi-spherical nucleus. Since the coexistence of cluster states and mean-field type states in 12 C, 16 O, 20 Ne, 24 Mg and 32 S is well established, ground states and entrance and decay channels of these nuclei have been also determined assuming spherical shapes and, then, their potential energies are calculated continuously from one spherical nucleus to two or three spherical aligned nuclei [27,28] using generalized elliptic lemniscatoids.

II. POTENTIAL ENERGY

To determine the energy of these light nuclear systems the GLDM has been used once again. It has previously been defined to calculate in an unified way and without new adjustment of parameters the fusion [23][24][25] and binary [26] and ternary [27,28] fission barriers, the barriers against α [29] and cluster emissions [30].

The GLDM energy is the sum of the volume, surface, Coulomb, and nuclear proximity energies. This proximity energy term is still often neglected because it appears only where there are deep necks or crevices in strongly deformed compact nuclear one-body shapes or between two separated spherical or ellipsoidal nuclei. It does not contribute to the mass formula or to the energy of elongated shapes with very shallow necks. In contrast it plays a main role to reproduce the fusion barriers beyond the pure unrealistic Coulomb peak, the fission barriers through quasimolecular shapes and the energy of nuclear molecules. For example, the proximity energy reaches -9.4 MeV between two α particles at the contact point. The GLDM and particularly the proximity energy term are detailed in Refs. [22,23].

This macroscopic approach is complementary to the microscopic mean-field studies which focalize on the variations appearing in the nuclear densities of one-body nuclear systems and do not consider explicitly separated multi-body shapes and usual clearly defined molecular structures.

III. 12 C NUCLEUS

Without assuming α clustering, calculations using Antisymmetrized Molecular Dynamics and Fermionic Molecular Dynamics have led for the shapes of the different states of 12 C to triangular α-molecules with different angles allowing the reproduction of the low-lying spectrum of 12 C [31][32][33]. Using effective field theory and Monte Carlo ab initio lattice calculations it has been found that the 12 C ground state and the first excited state 2 + 1 state have a compact triangular configuration while the Hoyle state and the second excited 2 + 2 state have a "bent-arm" or obtuse triangular configuration of α clusters [34]. These theoretical predictions are strengthened by the recent observation of a new high spin 5 -state at 22.4 MeV compatible with a ground state rotational band of an oblate equilateral triangular spinning top with a D 3h symmetry characterized by the sequence 0 + , 2 + , 3 -, 4 + -, 5 -but the Hoyle state is then interpreted as the band head of the A symmetric stretching vibration or breathing mode of the triangular configuration [14]. Therefore the structure of the Hoyle state is still controversial [15].

To study these oblate ternary configurations within the GLDM three α particles have been placed at the tops on an isosceles triangle and later on they separate and move away from each other in keeping the same triangular configuration characterized by the angle θ (see Fig. 2). At the contact point the energy of the equilateral triangular shape is lower than the energy of the linear chain of three α (θ=180 deg.), the energy difference being 7.36 MeV. This is also in favor of an equilateral triangular configuration for the ground state and a more aligned chain for the Hoyle state (the energy is almost constant between 120 and 180 deg.). For the ground state the experimental rms charge radius is < r 2 > 1/2 = 2.47 fm. With the radius formula of the GLDM, at the contact point the rms radius is 2.43 fm for a triangular molecule and 3.16 fm for a linear chain. Furthermore experimentally the electric quadrupole moment is negative which is inconsistent with three-aligned α particles for the ground state shape [22].

IV. 16 O NUCLEUS Since for the ground state a tetrahedral configuration of alpha clusters is predicted [7,8] and for the first excited spin-0 state a square configuration [7] it is worthwhile to investigate these shapes within a GLDM. In Fig. 3 the energies of these two configurations are compared. At the contact point between the four spherical α particles the rms radius is 2.54 fm for a tetrahedron, 2.83 fm for a square (which is less compact than a tetrahedron) and 4.15 fm for a linear chain. Experimentally the rms charge radius of the ground state is < r 2 > 1/2 = 2.70 fm which seems to exclude a linear chain configuration for the ground state. The binding energy is higher for the tetrahedral configuration than for the square shape since for these molecular configurations the proximity energy plays the main role and there are six bonds for the tetrahedron and only four for the square. On the contrary, the Coulomb repulsion (which is small) is lower for the square at the contact point. The energy difference is 13 The L-dependent energies of the tetrahedron and square are shown in Fig. 4 and Fig. 5. For the tetrahedral shape the relative energies at the contact point are respectively 0, 1.3, 4.4, 9.3 and 16 MeV for L = 0, 2, 4, 6 and 8 and for the square 0, 1.1, 3.5, 7.4 and 12.6 MeV for L = 0, 2, 4, 6 and 8 .

Since the ground state is also seen as double closed shell wave function and several low-lying excited states are described within the 12 C+ 4 He cluster model [START_REF] Horiuchi | Cluster in Nuclei[END_REF] the potential energies of the 12 C+ 4 He, 8 Be+ 8 Be, and linear 6 Li+ 4 He+ 6 Li systems have been determined assuming a spherical shape for the compound nucleus and each cluster (see Fig. 6). The different threshold energies are : 7.16 MeV for Q4 He+ 12 C , 14.44 for Q 4α , 14.62 for Q8 Be+ 8 Be , and 35.34 for Q6 Li+ 4 He+ 6 Li . The top of the barrier corresponds to separated nuclei maintained in unstable equilibrium by the balance between the repulsive Coulomb forces and the attractive nuclear proximity forces. In the 12 C+ 4 He channel quasimolecular one-body shapes have almost the same energy than the spherical nucleus. Experimentally the break-up of 16 O (at 4.5 GeV/nucleon) in two α's and a 8 Be has been observed using nuclear emulsions [35].

V. 20 NE NUCLEUS

For 20 Ne the pentagon, trigonal bipyramid and square pyramid shapes have been investigated with the GLDM. The energies of these three configurations are compared in Fig. 7. At the contact point the rms radius is 2.76 fm for a trigonal bipyramid, 2.79 fm for a square pyramid and 3.29 fm for a pentagon. The experimental rms charge radius is < r 2 > 1/2 = 3.01 fm far below the rms radius of a linear chain. The binding energy is higher for the trigonal bipyramid than for the square pyramid and the pentagon. The proximity energy at the contact point between two α's increases the binding energy and acts five times in the pentagon, eight in the square pyramid and nine times for the trigonal bipyramid. The Coulomb energy varies in the other sense. The energy difference between the trigonal bipyramid and the square pyramid is 21.3 MeV and 15.3 between the square pyramid and the pentagon at the contact point, while Q 5α = 19.17 In 20 Ne the ground band states contain the 16 O+ 4 He component at most 70% [START_REF] Horiuchi | Cluster in Nuclei[END_REF]. The potential energies of the 16 O+ 4 He, 12 C+ 8 Be, 10 B+ 10 B, and linear 8 Be+ 4 He+ 8 Be systems have been calculated assuming spherical shapes for all the nuclei (see Fig. 11). The different threshold energies are : 4.73 MeV for Q16 O+ 4 for Q8 Be+ 4 He+ 8 Be , and 31.14 MeV for Q10 B+ 10 B . In the 16 O+ 4 He channel quasimolecular one-body shapes have almost the same energy than the spherical nucleus and the minimum has a cluster structure corresponding roughly to the two 4 He and 16 O nuclei in contact. Experimentally the break-up of 20 Ne (at 3.65 GeV/nucleon) with the emission of five α's (partially as 8 Be) has been registered in nuclear emulsions [35].

VI. 24 MG NUCLEUS

For 24 Mg the energies of the hexagonal and octahedral α-molecules are indicated in Fig. 12. For the ground state the experimental rms charge radius is < r 2 > 1/2 = 3.06 fm. At the contact point the rms radius is 3.79 fm for an hexagon, and 2.85 fm for an octahedron which seems to exclude the planar configuration and the linear chain as possible ground state shapes.

More generally the rms radii given by the GLDM at the contact point of the equilateral triangle, tetrahedron, trigonal bipyramid or square pyramid and octahedron are slightly lower than the experimental rms radii of the ground states of the 12 C, 16 O, 20 Ne and 24 Mg nuclei. Keeping in mind that the formula used in the GLDM leads to a low value of the nuclear radius one may consider that the contact point of these three-dimensional shapes corresponds roughly to the ground state (within the cluster picture) and then to the minimum of the potential energy even though real minima do not appear on the curves since the very distorted one-body shapes corresponding to nascent several fragments still linked together are not considered.

For 24 Mg the binding energy is higher for the octahedral configuration than for the hexagonal shape since there are twelve bonds for the octahedron and only six for the hexagon. The electric quadrupole moment of the hexagon is -149.7 e fm 2 . The potential energies of the

VII. 32 S NUCLEUS

For 32 S the octogonal and cubic α-molecules have been studied. Their energies are displayed in Fig. 14. The experimental rms charge radius of the ground state is < r 2 > 1/2 = 3.26 fm. At the contact point the rms radius is 4.85 fm for an octogon, and 3.37 fm for a cube which excludes the planar and linear configurations. The binding energy is higher for the cubic molecule than for the octogonal shape since there are twelve bonds for the cube and only eight for the octogon. The electric quadrupole moment of the octogon is -345.3 e fm 2 .

The potential energies of the

VIII. BINDING ENERGY

From the experimental binding energies it is known that they can be reproduced within the molecular structures by the sum of the binding energy of n alphas plus the number of bonds multiplied by around 2.4 MeV.

B(

12 C) = 3 × B(α) + 3(bonds) × 2.42 M eV. B( 16 O) = 4 × B(α) + 6(bonds) × 2.41 M eV. B( 20 N e) = 5 × B(α) + 8(bonds) × 2.40 M eV. B( 24 M g) = 6 × B(α) + 12(bonds) × 2.37 M eV. (1)
From the GLDM it is difficult to explain this value of 2.4 MeV per bond since it does not correspond to the sum of the proximity energy and the mean Coulomb repulsion by bond.

The binding energy of these nuclei may also be calculated within the GLDM and a core+α cluster model since the energy corresponds to the sum of the binding energies of one alpha and the one of the daughter nucleus plus roughly the Coulomb energy and the proximity energy between the two nuclei. (2)

IX. SUMMARY AND CONCLUSION

Within an α-particle model approach the energy of the 12 C, 16 O, 20 Ne, 24 Mg and 32 S nuclei has been calculated assuming different α-molecule shapes : linear chain, triangle, square, tetrahedron, pentagon, trigonal bipyramid, square pyramid, hexagon, octahedron, octogon and cube. Within a macroscopic mean-field approach the potential barriers governing the entrance and decay channels of these nuclei via alpha emission or absorption as well as more symmetric binary and ternary reactions have also been compared.

The rms radii of the prolate chains differ from the experimental rms radii of the ground states. The binding energies of the three-dimensional shapes at the contact point are higher than the binding energies of the planar configurations. The core+α cluster configuration leads always to the lowest potential barrier. The binding energy of these 4n-nuclei can be determined within the sum of the binding energy of n alphas plus the number of bonds multiplied by 2.4 MeV or by the sum of the binding energies of one alpha and the one of the daughter nucleus plus the Coulomb energy and the proximity energy between the two fragments. Further experimental studies are highly desirable to better know the shape of these nuclei and the validity and limit of the α-particle molecule model.

FIG. 1 :

 1 FIG. 1: Planar and three-dimensional molecular shapes.

FIG. 2 :

 2 FIG. 2: (Color online) Potential energy of an isosceles triangular α-molecule as a function of the angle θ (deg.) and the root-mean-square radius Q.

FIG. 3 :

 3 FIG.3: Potential energies of a square and tetrahedral configurations from the contact point as a function of the rms radius.

FIG. 4 :

 4 FIG.4: Potential energy of the α-tetrahedron as a function of the angular momentum (in unit) and rms radius.

FIG. 5 :

 5 FIG. 5: Potential energy of the α-square as a function of the angular momentum (in unit) and rms radius.

FIG. 6 :

 6 FIG. 6: Potential barriers governing the 12 C+ 4 He, 8 Be+ 8 Be, and linear 6 Li+ 4 He+ 6 Li nuclear systems versus the distance between the mass centers (at L = 0).

FIG. 7 :

 7 FIG. 7: Potential energies of a pentagon, a trigonal bipyramid and a square pyramid from the contact point as a function of the rms radius.

FIG. 8 :

 8 FIG. 8: Potential energy of the α bipyramid as a function of the angular momentum (in unit) and rms radius.

  He , 11.98 for Q8 Be+ 12 C , 19.35

FIG. 9 :

 9 FIG. 9: Potential energy of the α square pyramid as a function of the angular momentum (in unit) and rms radius.

FIG. 10 :

 10 FIG. 10: Potential energy of the α pentagon as a function of the angular momentum (in unit) and rms radius.

FIG. 11 :FIG. 12 :

 1112 FIG. 11: Potential barriers governing the 16 O+ 4 He, 12 C+ 8 Be, 10 B+ 10 B, and linear 8 Be+ 4 He+ 8 Be reactions versus the distance between the mass centers (at L = 0).

FIG. 14 :FIG. 15 :

 1415 FIG. 14: Potential energies of an octogonal molecule and a cubic molecule from the contact point as a function of the rms

B( 12 C

 12 ) = B( 8 Be) + B(α) + 7.37 M eV. B( 16 O) = B( 12 C) + B(α) + 7.16 M eV. B( 20 N e) = B( 16 O) + B(α) + 4.73 M eV. B( 24 M g) = B( 20 N e) + B(α) + 9.32 M eV.

  16 O+ 8 Be,12 C+ 12 C, 8 Be+ 8 Be+ 8 Be, and 10 B+ 4 He+ 10 B systems are displayed in Fig. 13. The different Q values are : 9.32 MeV for Q4 He+ 20 Ne , 13.93 for Q12 C+ 12 C , 14.14 for Q8 Be+ 16 O , 28.48 for Q 6α , 28.76 for Q8 Be+ 8 Be+ 8 Be , and 40.46 for Q10 B+ 4 He+ 10 B .

  28 Si+4 He,24 Mg+ 8 Be,20 Ne+ 12 C, and16 O+16 O systems are displayed in Fig. 15 . The different threshold energies are : 6.95 MeV for Q4 He+ 28 Si , 16.54 for Q16 O+ 16 O , 17.02 for Q8 Be+ 24 Mg , 18.97 for Q12 C+ 20 Ne , 30.96 for Q12 C+ 8 Be+ 12 C , 34.17 for Q14 N + 4 He+ 14 N , and 45.42 for Q 8α . The energy of the 28 Si+ 4 He one-body nucleus is relatively constant till the spherical nucleus allowing the cohabitation of different quasimolecular shapes. The superdeformed band contains the 16 O+ 16 O component by about 44 % [5]. Potential barriers governing the 16 O+ 8 Be, 12 C+ 12 C, linear 8 Be+ 8 Be+ 8 Be, and 10 B+ 4 He+ 10 B reactions versus the distance between the mass centers.

		45	24 Mg
	E (MeV)	15 25 35			C + C O + Be B + He +B
		5			Be + Be + Be
		-5
		2	6	10	14	18
				r (fm)
	FIG. 13:


Gianluca Borghini
email: borghini@dis.uniroma1.it

Pietro Aricò

Gianluca Di Flumeri

Ilenia Graziani
email: ilenia.graziani@gmail.com

Alfredo Colosimo

Serenella Salinari

Fabio Babiloni
email: fabio.babiloni]@uniroma1.it

Jean-Paul Imbert
email: jean-paul.imbert@recherche.enac.fr

Géraud Granger
email: geraud.granger@recherche.enac.fr

Railane Benhacene
email: railane.benhacene]@recherche.enac.fr

Alessia Golfetti
email: alessia.golfetti@dblue.it

Stefano Bonelli
email: stefano.bonelli@dblue.it

Simone Pozzi
email: simone.pozzi]@dblue.it

Skill, Rule and Knowledge-based Behaviors Detection during Realistic ATM Simulations by Means of ATCOs' Brain Activity

Keywords: EEG; Skill, Rule, Knowledge, ATM, ATCO. I

The aim of this work was to test a neuro-physiological methodology able to discriminate the Skill (S), Rule (R) and Knowledge (K) based cognitive control levels of Air-Traffic-Controllers' performing realistic traffic management tasks . The three categories of human behaviours have been associated to specific cognitive functions (e.g. attention, memory, decision making) already investigated with Electroencephalography (EEG) measurements. A link between S-R-K behaviours and expected frequency bands configurations has been hypothesized. Eventually, specific events have been designed to trigger S, R and K like behaviours and then integrated into realistic Air Traffic Management (ATM) simulations. A machine-learning algorithm has been used to differentiate the three different levels of cognitive control by using brain features extracted from the EEG rhythms of different brain areas, that is, the frontal theta and the parietal alpha activities. Twelve professional Air-Traffic-Controllers (ATCOs) from the École Nationale de l'Aviation Civile (ENAC) of Toulouse (France) have been involved in the study. The results showed that the algorithm was able to differentiate with high discrimination accuracy (AUC > 0.7) the three S-R-K cognitive behaviours during simulated air-traffic scenarios in an ecological ATM environment.

INTRODUCTION

According to the framework proposed by Rasmussen [START_REF] Rasmussen | Information Processing and Human-Machine Interaction: An Approach to Cognitive Engineering[END_REF], the terms Skill, Rule and Knowledge-based (S-R-K) refer to "the degree of conscious control exercised by the individual over his or her activities, depending on the degree of familiarity with the task and the environment". The S-R-K behaviours represent three dynamic and parallel cognitive levels of expertise, where the control of behaviour continuously shifts from a level to another one.

At the skill-based level, the behaviour is regulated by the lowest level of conscious involvement and is characterized by highly routinized and automated activities. In fact, skill-based mode refers to "the smooth execution of highly practiced, largely physical actions in which there is virtually no conscious monitoring". In the ATM environment, a large portion of the expert controller's observable behaviour is skill-based: cursor positioning, command entry, use of phraseology.

Rule-based behaviour is also activated in familiar work situations, but it is distinguished from skill-based behaviour, as "it requires some degrees of conscious involvement and attention. Situation assessment leads to recognition of which procedures apply to particular familiar situations". Events implemented at this level are typical control task, such as rerouting, conflicts detection and management, and coordination.

When faced with unfamiliar situations, where no solutions are already available, it is necessary to move to the knowledgebased level of behaviour. At this level, the User "carries out a task in an almost completely conscious manner. This would occur in a situation where a beginner is performing the task (e.g. a trainee at the beginning of its training) or where an expert is facing with a completely novel situation. In either such cases, the User would have to exert considerable mental effort to assess the situation, and his or her responses are likely to be slow. Also, after each control action, the User would need to review its effect before taking further action, which would probably further slow-down the responses to the situation" [START_REF] Embrey | Understanding human behaviour and error[END_REF]. This framework of human performance is a useful means to figure out how humans can deal with ambiguous situations, solve familiar or unfamiliar situations, quickly react to the environmental requests, and set new problems in an efficient and flexible way. It is also a powerful framework to orient design and evaluation of new interface system.

The end research goal of this study is to define quantitative, reliable and valid neuro-physiological indicators for the S-R-K levels. This paper presents the testing and validation of such indicators, using data collected from Air Traffic Controllers' brain activity. The development of the actual SRK mental classifier, to identify S-R-K behaviours in real time would be the next step of the research.

II. MATERIALS AND METHODS

A. Literature review

Two steps were performed to select which brain features to analyse:

-First, S-R-K levels of control were associated to specific cognitive functions, -Then a literature review was performed on neuroscience research, in order to identify which brain activity frequency bands were linked to the identified cognitive functions. Literature evidences show that an increase of electroencephalographic (EEG) power spectral density (PSD), especially over the frontal cortex, in the theta band (4 -7 Hz), and an EEG PSD decrease in the alpha band (8-12 Hz), over the parietal cortex, have been observed when:

-increase of required automated processes [3][4],

-increase of demands on executive control (attention and working memory) [START_REF] Gevins | Neurophysiological measures of cognitive workload during human-computer interaction[END_REF]- [START_REF] Jensen | Human gamma-frequency oscillations associated with attention and memory[END_REF],

-activation of decision-making processes, like resolution of conflicts and error detection [START_REF] Beulen | The role of theta oscillations in memory and decision making[END_REF], or problem solving [START_REF] Sandkühler | Deconstructing insight: EEG correlates of insightful problem solving[END_REF],

-increase of mental workload [START_REF] Borghini | Measuring neurophysiological signals in aircraft pilots and car drivers for the assessment of mental workload, fatigue and drowsiness[END_REF] and task complexity [START_REF] Gevins | Monitoring working memory load during computerbased tasks with EEG pattern recognition methods[END_REF].

Based on such evidences, the following hypotheses have been formulated:

-Skill-based behaviour: high parietal alpha activity increment with respect to the Rule and Knowledge behaviours.

-Rule-based behaviour: frontal theta activity increment and a lower parietal alpha rhythm increase than in the Skill-based condition.

-Knowledge-based behaviour: higher frontal theta activation than in the Rule and Skill conditions, and parietal alpha activity increment.

B. Experimental subjects

Twelve professional (age: 40.41±5.54) ATCOs from the École Nationale de l'Aviation Civile (ENAC) of Toulouse (France) have been involved in this study. They were selected in order to have a homogeneous experimental group in terms of age and expertise. They all participated to 5 sessions of onehour on the experimental platform, like the following: Training 1, Experiment 1 (with EEG recording), Training 2, Experiment 2 (with EEG recording), Training 3. These sessions were followed by a final experiment session, named Experiment 3, where data were collected. The experiments have also been attended by two External Expert ATCOs, and two Pseudo-Pilots, who have interacted with the ATCOs with the aim to simulate real-flight communications and to modulate specific S-R-K events. During the sessions, the Experts sat behind the controllers, listening to R/T communications, observing the radar display, monitoring and triggering SRK events and taking note of anything considered relevant. They gathered data both on the performance of the ATCOs, in terms of air-traffic management, and on how the Controllers reacted in the different S-R-K events.

C. Experimental ATM scenario

ATCOs have been asked to perform an ATM simulation using the research simulator hosted at ENAC (Figure 1). The ATM scenario included three levels of difficulty, easy, medium, hard, and lasted 45 minutes. The same experiment was also used to validate a EEG based workload index [START_REF] Aricò | Reliability over time of EEG-based mental workload evaluation during Air Traffic Management (ATM) tasks[END_REF]. The traffic complexity has been modulated by the number of aircraft in the controlled sector and the geometry of conflicts. Six S-R-K events (two for each type, S1, R1, K1, S2, R2, K2) have been inserted into the ATM scenario within coherent difficulty conditions (Figure 2). The S-R-K events have been designed to maximise the realism of ATC tasks (see the following section for more details). The system was calibrated recording ATCOs' brain activity in a Baseline condition (rest conditions, with closed and open eyes) and in a Reference condition (ATCOs looked at the radar screen without reacting, where two conflict-free flights were being presented). The calibration took place for each ATCO at the beginning of the simulation session.

D. S-R-K events

A Subject Matter Expert (SME) controller from the Ente Nazionale di Assistenza al Volo (ENAV, Rome, Italy) was involved in order to create realistic and not disruptive SRK events during the simulation. The events represented an attempt to induce ATCO behaviours associated with S-R-K levels during usual normal air traffic conditions. The following considerations apply to the design of the S-R-K events.

The S events were basic interactions with the interface, during the task execution. As the ATCOs participated to previous sessions, we were able to track their progress and make sure they had acquired a high level of proficiency and expertise in the use of the platform interface. This check was needed as not all interface interactions can be classified as Skill-based, only those that are actually carried out at that level. Controllers were asked to visualize the distance between two aircraft (Distance event) and to display the Flight Plan (FPL) trajectory of each aircraft present in the controlled sector (Display FPs).

The R events were mainly control-tasks and conflictsresolutions, during which controllers were also performing skill-events (interaction with the interface). In the two "conflict event" presented, Controllers had to detect and solve a conflict by using the menu of the interface and assigning new altitudes and headings. The hypothesis was that routine conflict detection task represents a familiar situation for ATCOs. Therefore, Controllers would recognize the correct procedures and familiar solutions and then to apply them to solve the conflict.

The K events integrated in the scenario were unusual situations. This uncertainty led the Controllers to analyse the situation and to find out the right procedure to cope with the unexpected event. In other words, the ATCOs initially had to analyse the unusual situation (problem setting at the Knowledge-based level) and then came back to the Rule-based level to select the right procedures (problem solving at the Rule-based level, without the need of developing a new solution). In the first Knowledge-based event, "deviation event", Controllers were expected to detect and understand that an aircraft was not following the route filled in the flight plan (FPL). Once contacted, the pilot would state that he was following the right FPL. Controllers needed to understand what was going on.

In the second Knowledge-based event "Unidentified Flying Object (UFO)", the Pseudo-Pilot reported an unknown-traffic detected by the Traffic Collision Avoidance System (TCAS) and a TCAS resolution advisory to avoid a mid-air collision. This unknown aircraft was not displayed on the Controller's radar image. The ATCO was expected to ask additional information to the Pseudo-Pilot. After the avoidance manoeuvre (descent), the Pseudo-Pilot would ask for his previous flight-level, which would display as not changed on the ATCO's HMI. The Controller would see neither the aircraft Figure 1. Experimental setup: prototypal ATCO working positions developed by ENAC (Toulouse, France) for a research simulator. The ATCO's brain activity has been recorded continuosly and S, R and K events have been marked in order to recognize them within the entire EEG recording.

responsible of the TCAS advisory nor the implementation of the avoidance manoeuvre.

Each event lasted for about 30 seconds. Due to the need of inserting SRK events into realistic ATM tasks, it was not possible to create "pure" SRK behaviours. While Skill events were basic interactions with the interface and the ATCO could be almost entirely focused on them, the same could not be done for the Rule and Knowledge levels. The Rule events were control tasks and conflicts resolutions, during which controllers were also performing at a skill level (having to interact with the interface to handle them). The Knowledge events involved the three levels: Skill + Rule + Knowledge. Considering the need of building realistic situations and taking into consideration the limitations of a simulation, it was possible to prepare events triggering a uncertainty state in controllers, in other words situations that were peculiar enough to make controllers focus on them to try and recognise a familiar situation. After this initial "what is going on?" state, controllers usually came back to the rule level, finding a procedure to solve the problem or deciding to ignore it. In the latter case, their interpretation was that it was pilot's responsibility or simply not impacting traffic safety.

E. Physiological signals recording and pre-processing

The neurophysiological signals have been recorded by the digital monitoring BEmicro system (EBNeuro system). The thirteen EEG channels (FPz, F3, Fz, F4, AF3, AF4, P3, Pz, P4, POz, O1, Oz, O2) and the EOG channel have been collected with a sampling frequency of 256 (Hz). All the EEG electrodes have been referenced to both the earlobes, grounded to the left mastoid, and the impedances of the electrodes were kept below 10 (kΩ). The bipolar electrodes for the EOG have been positioned vertically above the left eye. The acquired EEG signals have been digitally band-pass filtered by a 4th order Butterworth filter (low-pass filter cut-off frequency: 30 (Hz), high-pass filter cut-off frequency: 1 (Hz)) and the EOG signal has been used to artefacts remove eyes-blink from the EEG data by using the [START_REF] Gratton | A new method for off-line removal of ocular artifact[END_REF]. Although EEG is designed to record cerebral activity, it also records electrical activities arising from sites other than the brain. The recorded activity that is not of cerebral origin is termed "artifact" and can be divided into physiologic and extraphysiologic artifacts. While physiologic artifacts are generated from the patient, they arise from sources other than the brain (i.e. body). Extra-physiologic artifacts arise from outside the body (i.e. equipment, environment). For other sources of artefacts on the EEG signal, specific procedures of the EEGLAB toolbox, based on threshold methods have been used [START_REF] Delorme | EEGLAB: an open source toolbox for analysis of single-trial EEG dynamics including independent component analysis[END_REF]. In particular, three methods have been used for the artefacts rejection: the threshold criteria, the trend estimation and the sample-to-sample difference. In the threshold criteria the EEG epoch has been marked as "artefact" if the EEG amplitude was higher than ±100 (μV). In the trend estimation, the EEG epoch has been interpolated in order to check the slope of the trend within the considered epoch. If such slope was higher than 3 (no-physiological variation), the considered epoch has been marked as "artefact". The last check calculated the difference between consecutive EEG samples. If such difference, in terms of amplitude, was higher than 25 (μV), it meant that an abrupt variation (no-physiological) happened, thus it was marked as "artefact". At the end, the EEG epoch marked as "artefact" have been removed from the EEG recording with the aim to have a clean EEG signals from which estimate the brain parameters for the different analyses. The Power Spectral Density (PSD) has then been estimated by using the Fast Fourier Transform (FFT) in the EEG frequency bands defined for each subject by the estimation of the Individual Alpha Frequency (IAF) value [START_REF] Klimesch | EEG alpha and theta oscillations reflect cognitive and memory performance: a review and analysis[END_REF].

F. S-R-K estimation

The classification algorithm automatic stop Stepwise Linear Discriminant Analysis (asSWLDA, patent pending [START_REF] Aricò | A Method for the estimation of mental state, in particular of the mental workload and its device[END_REF]), developed by the "Sapienza" University of Rome's spinoff, BrainSigns, has been used to select the most relevant brain spectral features to discriminate the three S-R-K cognitive levels. In particular, the algorithm has been trained by using the brain areas and rhythms found in the scientific literature and described previously (frontal theta and parietal alpha bands). In this way, the algorithm has been trained with brain features extracted from one triplet of S-R-K events (S1, R1, K1) and then tested on the remaining triplet (S2, R2, K2) and viceversa. For each testing triplet, we calculated the Area Under Curve (AUC) values of the Receiver Operating Characteristic (ROC, [START_REF] Bamber | The area above the ordinal dominance graph and the area below the receiver operating characteristic graph[END_REF]) by considering couples between S-R-K distributions. The AUC values related to the discrimination accuracy between the three couples of conditions (S vs R, S vs K, R vs K) have been calculated and analysed for each Controller. It has to be underlined that an AUC of 1 means a perfect discrimination between the considered classes (S vs R, S vs K, R vs K). On the contrary, if the AUC is equal to 0.5, the algorithm is not able to discriminate the classes. More in general, if the AUC is higher than 0.5 and lower than 0.7, the classification is good, if it is higher than 0.7, the classification is optimum, in other word the classes can be discriminated.

G. Performed analyses

In order to test the effectiveness of the algorithm, for each couple of conditions (S vs R, R vs K, S vs K), we have compared the AUC distributions obtained from the experimental data of all the ATCOs (Measured AUC), with the same distributions centred on 0.5 (Random AUC), situation corresponding to the chance level. As stated before, an AUC of 0.5 means that the algorithm is not able to discriminate the two conditions. We compared the Random AUC distributions with the Measured AUC, by using three two tailed student t-tests (α=0.05), in order to demonstrate the reliability of the algorithm.

III. RESULTS

The area under curve (AUC) related to the three couples of conditions (S vs R, S vs K, R vs K) have been calculated and reported in figure 4, together with the AUC distribution centred in 0.5 (Random AUC). In particular, the results of the statistical tests highlighted that the Measured AUC distributions were significantly higher than the Random AUC distributions (p<0.001). In other words, the machine-learning algorithm was able to discriminate the S-R-K conditions high reliability (AUC > 0.7), thus providing information about the level of cognitive control of the ATCOs.

IV. DISCUSSION

The research hypothesis of this study was tested with positive results. The algorithm was able to differentiate significantly the ATCOs' cognitive control behaviours (induced by the ad-hoc designed scenario events) with an accuracy higher than 70%. This result should be taken with due consideration of the limitations of this study.

In the design of the ATM scenarios, we introduced S-R-K events compatible with the air traffic situation of that moment, keeping the ATM simulation as realistic as possible. For this reason, the S-R-K events did not fit perfectly with the Rasmussen's model. However, they fit our purpose of triggering skill-based, rule-based and a "what is going on" responses (the closest we could get to the Knowledge-based level with experts).

The aim of the analysis was not to identify moments or "pure Skill", or "pure Rule, "or pure Knowledge" within specific events, nor to develop a real-time SRK classifier. Our goal was to test the possibility of using brain activity to discriminate these cognitive control behaviours. In other words, the S, R and K events have been designed with the aim to investigate the possibility to define a metric, based on specific brain features, by which discriminating and quantitatively estimating the cognitive control behaviour (S, R or K) during the execution of an ATM task. The capability of distinguishing these levels is a pre-condition for the actual development of a real-time SRK classifier.

V. CONCLUSIONS

This study demonstrated that it was possible to assess with a high reliability the ATCO's cognitive control level (S-R-K) by monitoring her/his brain activity. To our knowledge, there are no corresponding studies in the existing literature.

Several studies mention the different information processing levels of Skill, Rule, and Knowledge, but we found no mention in these studies of the associated neurophysiological indicators. The aim of this study was to address this gap, by identifying neuro-physiological indicators that could potentially be used to discriminate the S, R and K levels.

The results represent a promising step further in the analysis of human behaviour and demonstrate the possibility of developing new HF tools able to discriminate, also in real-time, the level of operators' cognitive control during ecological tasks. Another possible use might be an online tool for triggering Adaptive Automations (AA, [START_REF] Byme | Psychophysiology and Adaptive Automation[END_REF]- [START_REF] Wilson | Performance enhancement with Real-Time Physiologically controlled Adaptive Aiding[END_REF]), in which the system behaves depending on the Operator's current level of cognitive control. The authors already implemented a similar solution, but only based on the real-time monitoring of the workload level. Finally, as the level of cognitive control during a task is related to the level of User's expertise, this tool can also be used to track the level of training reached by the User.

Figure 2 .

 2 Figure 2. The ATM scenario has been designed with different difficulty conditions (levels of complexity).. The S-R-K events have been selected within coherent difficulty conditions (in red and light-blue squares).

Figure 3 .

 3 Figure 3. Error bars (CI=.95) related to the Measured AUC and the Random AUC distributions, related to the three couples of conditions (S vs R, S vs K and R vs K).

Table 1 : Association between levels of performance and EEG bands.

 1

						No automated
						processes and long term memory (procedural) Executive control (attention and	High theta	Frontal	Af3-Af4 Fp1-Fp2 Af7-Fpz F1-F2 F6-F7-F8
					Knowl	working memory)
					edge	High Attention
						Decision-making (resolution of	Low alpha	Parietal	-2
						conflicts and error
						detection)
						Problem solving	High gamma	Parieto-occipital	-3
	SRK	Cognitive processes	Bands	Location	Channels 1
		High Automated
		processes and long
		term memory
		(procedural) Low Executive control (attention	Low theta	Frontal	Fc3-Fc4 F5-Fc6 F8
		and working
	Skill	memory)
		Low Attention			C3-C4
		No Decision-making (resolution of conflicts and error detection)	High alpha	Posterior	C5-C6 C1-Cp2 P1-P2 P5-P6 T7-T8
		No Problem solving			O1-O2
		Less automated
		processes and long
		term memory
		(procedural) than
	Rule	Skill level More executive control (attention and working memory) than Skill level	Increased theta respect to Skill level	Frontal	F1-F2 Fc3-Fc4 F5-Fc6 F7-F8 Af7-F6
		More Attention than
		Skill level
		No Decision-making (resolution of conflicts and error detection)	Decrease d alpha respect to Skill	Parietal	P1-P2 P5-P6 Cp3-Cp4
		No Problem solving	level
	1 For the mapping between EEG channels and Brodmann
	areas, see http://www.brainm.com/software/pubs/dg/BA_10-
	20_ROI_Talairach/nearesteeg.htm

No specific channels available from the literature review for this specific level of performance.

No specific channels available, just generic identification of involved brain areas.

ACKNOWLEDGMENT This work is co-financed by EUROCONTROL on behalf of the SESAR Joint Undertaking in the context of SESAR Work Package E -NINA research project (www.nina-wpe.eu).


Serge Fenet
email: serge.fenet@liris.cnrs.fr

Yannick Perret
email: yannick.perret@liris.cnrs.fr

Julien Salotti
email: julien.salotti@insa-lyon.fr

Extract space-time dynamics from sensor network to build urban traffic prediction model: a machine learning point of view

Introduction and context

Urban transport, while being essential for citizens to perform their daily activities, also constitutes one of the major sources of urban pollution (global emissions, local air quality, noise) and physical accidents (the two thirds of them taking place in cities), directly affecting humans health. Moreover, the economic impact of traffic jams on goods transportation within cities reduces the efficiency of urban delivery process and impair its' economical aspect. In spite of great efforts made to favor modal report from car to other public transportation systems, the quest for an environmentally sustainable urban transport is a common and urgent challenge for all major cities in Europe. In these circumstances, and in order to (i) tackle the challenge of sustainable urban mobility, (ii) efficiently implement decision support tools, and (iii) exploit data allowing the assessment of policies and their resulting effects, urban planners need models.

Along the years, different types of urban models have been developed, ranging from the static and aggregate land use-transportation interaction (LUTI) models , to more recent bottom-up, activity and agent-based simulation. In the context of the Optimod'Lyon project, this work focuses on building a traffic prediction model of road traffic within the city of Lyon by using the Grand Lyon historical measures from more than 650 sensors between the year 2007 and now. This global model will be composed of a predictive model (gray box model that preserves dynamics) and an explanatory model (white box model that explicitly identify space-time features).

This paper aims at presenting the ongoing process of exploration of these data and the building of these models. Each section of this abstract highlight a potential barrier, and quickly presents the possible tracks a modeller could use to overcome them. The main conclusion we wish to convey is that, as almost every question is a research field in itself, important choices have to be made at every step, and there can be no universal model. The space available being short in this abstract, we focus here on textual description rather than graphical illustrations that could better highlight the arguments.

Data features

With 654 sensors gathering 240 measures of car count and lane occupation rate per day during more than 1700 day, a final amount of more than 540 million measures is both a blessing and a curse. These data contain vast amounts of information that we are still extracting, but also exhibit both noise and missing values as sensors can be faulty or suffer failure. Depending on the size of missing values blocks, such problems can be solved with interpolation (on short scale), multiple imputation (on larger scale), or by using clustering algorithms and partial deletion in order to reduce the available data to a dataset having no missing values. Artificial noisiness of data is more treacherous than missing values as it is much harder to identify: absurd values can be easily detected by analyzing anomalous deviation from a dynamically learnt profile, but abnormal plausible measures are much harder to identify.

Traffic data are the results of the dynamics of the city as a complex unknowable system, and thus exhibit both space and time components. These two components can be used as main exploration direction by using different tools.

Sensor clustering

Road sensors are distributed among road segments all through the city, and pick up different signals: some of them are located on wide circulating segments, others are situated on narrow street. They can be situated near important crossing points, or along continuous avenues. This heterogeneity leads to different data dynamics, that can be used to cluster the sensors. The idea is to group road segments sharing the same dynamics (same occurrences of the variation of a measure) independently of the measured value.

To do so, we first convert time domain data to frequency domain data by computing the Discrete Fourier Transform of the time series of each sensor, then feed this frequency representation to standard clustering methods. In this case, the optimal number of cluster K is firstly computed by using the Mean Shift algorithm, then the algorithm K-Means is used with the optimal value of K (that can be proved by computing standard clustering quality indices like the 'within cluster sum of square'). It is also possible to sweep different value of K and use expert knowledge to choose the value that matches the most with the expert perception.

Space influence on data dynamics

An important distinguishing feature of our data is the ever-present dependency between road segments: the current state of a given segment will not only be influenced by it's own past, but also by the past of neighbouring segments within a horizon that will grow with the passing time. This space-time dependency is an important trigger of the non-linear behaviour of road traffic, and the evaluation of the dependency of each sensor to the others is thus an important component of the model. Moreover, this information can help us to identify unnecessary sensors -those which signal can be fully reconstructed from distant sensors-, or allow us to build 'virtual sensors' providing economical alternatives to unpractical or costly measurements.

A way to discover such cross-correlations is to use Dynamic Bayesian Networks. This probabilistic directed acyclic graphical model, whose edges represent conditional dependencies, will identify the minimum set of sensors necessary to explain the data and their probabilistic relationship. This graph can then be compared with the real distance graph with matrices correlation test (like Mantel test) to explore the influence of spatial city structure on the traffic.

Time distribution

The signal of each sensor is generated by non linear dynamic equations, leading to time-changing variance, asymmetric cycles, varying thresholds and higher-moment structures. However, each signal exhibit a strong low-frequency structure along with higher frequency random noise which color still has to be determined. It is then possible to extract long term low-frequency patterns on the one hand, and a description of noise on the other. As colored noise is indistinguishable from chaos, we can use Discrete Wavelet Transform to extract high-frequency stochasticity description (particularly noise envelope) at different time scales from sensor data. Such a noise model can then be used to reinject high-frequency noise into low-frequency forecasts.

Non linear deterministic dynamical systems tools

Non linear times series analysis is an old field at the crossing of statistical physics and chaos theory. From a computer science point of view, these series can be represented in a multi-dimensional phase space rather than in the time or the frequency domain, expressing all properties in terms of local quantities and space neigbourhood relations. This paradigm shift pave the way to many tool allowing to explore stationarity (with recurrence plots and stationarity tests), graphical embedding in low-dimension representation (with time delay coordinates, for example), non linear prediction (with threshold autoregressive model), non linear noise reduction (with phase space projection), and the creation of surrogate data (with constraints randomisation) when we have to deal with missing values. All these tools can help us to, first, distinguish chaotic time series from purely random data, and secondly assess the fact that the data are the product of a deterministic system that can be modelled.

5 Our current baseline: simple N -weighted learning from the past Building a 'naive' baseline prediction method is an important starting task: it allows to have a set of reference results to compare to more sophisticated models, and so to evaluate the effective gain that must stem from the increased complexity. We implemented a N -weighted learning from the past method based on the idea that traffic behavior at a given time is often similar to traffic that occurred in the past and should then lead to a similar evolution in the near future. This method defines a distance measure on near past events based on a N -weighted calculus. It searches in the past the situations most similar to the current situation. It then takes the M most-fitting situations and uses the corresponding 'futures' to build prediction values for the current time. This set of situations is also used to compute an estimation of the variance of past data, allowing to also predict an expected variance around our predictions. This method has several parameters that need to be tuned: values for N and M , weights for the distance, weights for the combination of the M situations to create the prediction... Traffic can have very different dynamics depending on the day of the week, the current time in the day, the weather, etc. So, we trained our system to learn the best set of parameters for each of these different influences, giving us a large set of dedicated parameters to use in different situations. As explained previously, traffic data has both low-frequency (tendancy) and high-frequency (variability) component. That's why our method works on low-pass filtered data: it predicts the tendencies and gives an estimation of the noisy component, allowing to check if current data is within or outside the predictable variations. This latter case can thus be used as an indicator for an unexpected situation (road accident, etc.).

Conclusion and future work

This abstract has very briefly presented the directions we are currently exploring in order to build models describing and explaining the dynamics and stochasticity of the Lyon road traffic by focusing on different features of the available data. The firsts model are already being evaluated, and we plan to combine their multiple predictions by using machine learning methods like bagging (averaging predictions or majority voting from each model), boosting (developing multiple models in sequence by assigning higher weights for the training cases that are difficult to classify), or random forests. In order to evaluate their expressive power they will be compared with a naive N -weighted learning algorithm that we also presented.

Fig. 1 .

 1 Fig. 1. Expressive power of naive baseline 'N -weighted learning from the past'