Samaneh Nasiri

Ghosheh Bolagh

Mohammad Bagher Shamsollahi

Christian Jutten

Marco Congedo

Unsupervised Cross-Subject BCI Learning and Classification using Riemannian Geometry

The inter-subject variability poses a challenge in cross-subject Brain-Computer Interface learning and classification. As a matter of fact, in cross-subject learning not all available subjects may improve the performance on a test subject. In order to address this problem we propose a subject selection algorithm and we investigate the use of this algorithm in the Riemannian geometry classification framework. We demonstrate that this new approach can significantly improve cross-suject learning without the need of any labeled data from test subjects.

Introduction

Predicting the stimulus from concurrent brain neuroimaging data is an approach that can be used to understand underlying mental processes [START_REF] Lotte | Regularizing Common Spatial Patterns to Improve BCI Designs: Unified Theory and New Algorithms[END_REF]. It is well known that brain electroencephalographic (EEG) signals are subject-specific, thus brain decoding models are traditionally designed individually: training and test data belongs to the same subject [START_REF] Lotte | Regularizing Common Spatial Patterns to Improve BCI Designs: Unified Theory and New Algorithms[END_REF]. However, collecting sufficient labeled data from new subjects for learning a classifier is an expensive and time consuming procedure, jeopardizing the participants' willingness to use the system [START_REF] Lotte | Learning from other subjects helps reducing Brain-Computer Interface calibration time[END_REF]. Given the abundance of labeled data from other subjects, it is tempting to use them for training a classifier. Nevertheless, not all such training subjects may improve the performance on a given test subject because of inherent inter-subject variability [START_REF] Lotte | Learning from other subjects helps reducing Brain-Computer Interface calibration time[END_REF]. To address this problem, we propose an algorithm, named Rank Of Subjects (ROS), which ranks training subjects and selects a relevant subset. The proposed method has the same structure as the subject selection algorithm proposed in [START_REF] Lotte | Regularizing Common Spatial Patterns to Improve BCI Designs: Unified Theory and New Algorithms[END_REF]. The relevant subjects are selected through the maximization of the accuracy that is obtained by applying the classifier trained on data from all subjects to the unlabeled data of the test subject.

In [START_REF] Barachant | Multiclass Brain-Computer Interface Classification by Riemannian Geometry[END_REF] a multi-class BCI classification framework based on Riemannian Geometry has been proposed. The idea is to use appropriate forms of data covariance matrices as features and classifying using the simple concepts of distance and center of mass of these covariance matrices on a Riemannian manifold [START_REF] Congedo | EEG Source Analysis[END_REF]. Thanks to the use of an appropriate metric, this approach has displayed excellent crosssubject generalization capabilities, besides robustness to EEG artifacts, outliers and mislabeling [START_REF] Congedo | EEG Source Analysis[END_REF].

In this article, we address the problem of cross-subject training without assuming knowledge of labels from the test subjects. The proposed method is a combination of previously proposed subject selection algorithms and some fundamental concepts of Riemannian Geometry. The performance of our algorithm is asssessed on the open "DecMeg2014" Kaggle dataset (www.kaggle.com).

Rank Of Subjects

Due to inter-subject variability, the distribution of data in the training set may be more or less different from the test subject. A cross-subject classifier may be trained using only those training subjects that are similar to the test subjct, according to some criterion [START_REF] Lotte | Regularizing Common Spatial Patterns to Improve BCI Designs: Unified Theory and New Algorithms[END_REF]. We propose to rank the training subjects and select a subset of them according to Algorithm 1. In this algorithm, first we construct virtual labels for the test subject by training a SVM (support-vector machine) classifier using labeled data from all training subjects. Then, the most relevant training subjects are selected by maximizing the accuracy obtained on the virtual labels. Accuracy is returned by the function J(X k ) when the trained SVM classifier on X k is applied on test data. Finally, among the available N s training subjects, we select the subset of size N R featuring highest accuracy. Step 1 (Inclusion)

Algorithm 1 Rank Of Subjects (ROS)

6:

[x + , accuracymax] = arg max x∈[{X l s } Ns s=1 -X k ] J(X k + x)
7:

X k+1 = X k + x + , k = k + 1
8:

accuarcy k = accuracymax

9:

Step 2 (Exclusion) 10:

if k > 2 then
11:

[x -, accuracymax] = arg max X k J(X k -x)
12:

if accuracymax > accuarcy k-1 then 13:

X k-1 = X k -x -, k = k -1
14:

accuarcy k-1 =
accuracy k 22: ROS = X Best N 23: return the first N R subjects
In order to enhance the signal-to-noise ratio (SNR) of EEG evoked potentials, we use a standard spatial filtering approach. Let X i ∈ C×N denote a trial indexed by i, with C the number of channels, N the number of time samples and y i the class label of the trial. For each class, a set of N f ilter spatial filters are built. The spatial filters are an adaptation of the well-known common spatial pattern to evoked-potential data [START_REF] Rivet | xDAWN Algorithm to Enhance Evoked Potentials: Application to Brain?Computer Interface[END_REF], here implemented following the winner of the "DecMeg2014" competition [START_REF] Barachant | MEG decoding using Riemannian Geometry and Unsupervised classification[END_REF]. The average trial of the class k is denoted by P (k) [START_REF] Barachant | MEG decoding using Riemannian Geometry and Unsupervised classification[END_REF]:

P (k) = 1 |I (k) | i∈I (k) Xi, (1)
where I (k) = {i | y i = k} is the set of indices of the trials belonging to class k.

The spatial filter w ∈ C×1 for each class k solves the following optimization problem:

w * = arg max w w T P (k) P (k) T w w T XX T w , ( 2
)
where X is the matrix holding the continuous EEG recording (here we consider the concatenation of all trials from all classes). This equation is a generalized Rayleigh quotient, the solutions to which can be found as the eigenvevtor matrix of matrix (XX T ) -1 (P (k) P (k)T ). By construction, the C resulting eigenvectors are ranked by SNR. For each class, only the first N f ilter vectors are selected. Therefore, for each class k, the spatial filters is W (k) ∈ C×N f ilter . Spatial filtering operation is simply done by linear projection of the trial by the matrix W = [W (0) , W (1) , . . . , W (K) ] ∈ C×(K * N f ilter ) , which is the aggregation of the K spatial filters for each class in a single matrix, such as

Zi = W T Xi. (3)
The usual covariance matrices do not hold the temporal structure of ERP trials. Therefore, in order to keep all spatial and temporal information a special estimation of the covariance matrix is used [START_REF] Congedo | EEG Source Analysis[END_REF]. We build a new trial Zi ∈ (2 * K * N f ilter )×T by concatenation of the spatially filtered response obtained by averaging several single trial responses of one class P (k) and the spatially filtered trial Z i [START_REF] Barachant | MEG decoding using Riemannian Geometry and Unsupervised classification[END_REF]:

Zi = W (0) T P (0) , W (1) T P (1) , . . . , W (K) T P (K) , Zi T . (4)
These "super" trials are used to build the feature covariance matrices. The feature covariance matrices are obtained simply by using a Sample Covariance Matrix (SCM) estimator [START_REF] Barachant | Classification of covariance matrices using a Riemannian-based kernel for BCI applications[END_REF], such as

Σi = 1 N Zi ZT i . (5)
The covariance matrices in [START_REF] Congedo | Approximate Joint Diagonalization and Geometric Mean of Symmetric Positive Definite Matrices[END_REF] belong to the space of Symmetric Positive Definite (SPD) matrices. The space of SPD matrices forms a Riemannian manifold of nonpositive curvature [START_REF] Barachant | Classification of covariance matrices using a Riemannian-based kernel for BCI applications[END_REF]. Therefore, we can use tools issued from differential geometry on Riemannian manifolds to manipulate them. Riemannian Distance: For any two covariance matrix Σ 1 and Σ 2 , the Riemannian distance according to the Riemannian metric is given by [START_REF] Moakher | A differential geometric approach to the geometric mean of symmetric Positive-Definite matrices[END_REF] δR(Σ1, Σ2)

= log Σ -1/2 1 Σ2Σ -1/2 1 F = C c=1 log 2 λc 1/2 (6)
where λ c , c = 1 . . . C are the real eigenvalues of

Σ -1/2 1 Σ 2 Σ -1/2 1
and C the number of channels. This distance is Affine-invariant [START_REF] Barachant | Multiclass Brain-Computer Interface Classification by Riemannian Geometry[END_REF], meaning that is invariant with respect to similar and congruent transformation, but also to inversion.

Riemannian Mean: The Riemannian geometric mean of I covariance matrices (denoted by G(.)), also called Fréchet or Karcher mean, is the point on the manifold minimizing the dispersion [START_REF] Barachant | Multiclass Brain-Computer Interface Classification by Riemannian Geometry[END_REF], i.e. G (Σ1, . . . , ΣI ) = argmin

Σ I i=1 δ 2 R (Σ, Σi) . ( 7
)
There is no closed form expression for this mean for I > 2, however a gradient descent in the manifold can be used in order to find the solution [START_REF] Congedo | Approximate Joint Diagonalization and Geometric Mean of Symmetric Positive Definite Matrices[END_REF]. Train spatial filters given the labels yi,n of the trial i at the iteration n.

5:

Apply the spatial filters on the trials

6:

Estimate special form covariance matrices Σi

7:

Obtain K mean covariance matrix for each class:

Σ (0) G , . . . , Σ (K) G
, Eq.( 7)

8:

Classify each trial according to the Riemannian distance 9:

ŷ = argmin k δ R (Σ (k) G , Σ i ) , Eq.(6)
10: end while 11: return ŷ

Results

We evaluate the proposed method on the magnetoencephalography (MEG) dataset used in the "DecMeg2014" Kaggle competition. This dataset is comprised of 16 subjects. During the experiment participants observed two visual stimuli: face and scrambled face. Approximately 580-590 trials have been recorded for each subject. The duration of each trial was 1.5 seconds, with the stimulus presented at time 0.5 second. The class label was either Face (class 1) or Scramble Face (class 0).

As pre-processing, the original MEG recording (306 channels) has been downsampled at 250Hz and high-pass filtered at 1Hz. We use the SV M light toolbox for training SVM classifier and constructing virtual test labels. The standard SVM uses the default parameter tuning. In the ROS algorithm, we select the eight most relevant subjects (half of available training subjects). We compare result of standard SVM classifier with ROS and without ROS. The performance of the proposed method is evaluated by means of percent classification accuracy on the test data using a leave-one-out proceure (LOO).

The first column of Table 1 reports the accuracy of a standard SVM classifier. In this method we pool all training data from all training subjects and train a SVM classifier on such labeled data and then apply on test data. This is a generic classifier and it achieves an accuracy of 69.85 % . For the second column (SVM+ROS), we train SVM classifier on training data from a selected subset of training subjects as per the ROS algorithm; this generic classifier reaches 71.47% accuracy. In the third column (MDRM), for each class of test data, a set of four spatial filters are built as per Eq.( 1), where in the equation P (k) is constructed based on virtual labels. We estimate covariance matrices by Eq.( 5). Each trial is classified according to the Riemannian distance from two mean covariance matrices for each class Σ G . This procedure is iterated until convergence. Results of MDRM [START_REF] Barachant | MEG decoding using Riemannian Geometry and Unsupervised classification[END_REF] and the combination ROS+MDRM are provided in third and last column, respectively. The combination ROS+MDRM achieves a much higher performance (77.94%) as compared to the other methods. The performance improvement is 2.14% compared to MDRM [START_REF] Barachant | MEG decoding using Riemannian Geometry and Unsupervised classification[END_REF]. The results show 10 % improvement compared to [START_REF] Olivetti | MEG decoding across subjects[END_REF] which used another cross-subject transfer learning approach to classify this same dataset.

Conclusion

In this paper we have proposed a method for brain decoding with cross-subject learning. It is well-known that EEG and MEG signals are very specific to each subject. As a result, establishing a generic model featuring high classification performance is a very difficult task due to large inter-variability between subjects. We proposed a ROS algorithm for ranking automatically the relevant training subjects and selecting the best training subset. By combination of this method with Riemannian Geometry we have simply classified each trial based on distance of each trial from the two class-related mean covariance matrices. By evaluating the proposed algorithm on the MEG dataset of the "DecMeg2014" competition we have shown that this approach can outperform other methods. In future works the methods will be tested on other datasets and we will study how the mismatching between training and test subjects can be reduced.

1 :

 1 Train a model by concatenated labeled data from all source subjects 2: Generate virtual label Vu by applying trained model on target data 3: Initialize accuracy 0 = 0, K = 1, X0 = {}, 4: while n < Ns do 5:

Algorithm 2 1 :

 21 Rank Of Subjects and Minimum Distance to Riemannian Mean (ROS and MDRM) Input: X u t Unlabeled Signal from Target Subject Input: X l s Ns s=1 Labeled Signal from Ns Source Subjects Input: Source Subjects who are more relevant to Target Subject as selected by the ROS algorithm Output: The label of target subject Train a classifier on labeled data from relevant source subjects 2: Initialize target labels by applying the designed classifier to Target Subject 3: while y i,(n+1) = yi,n do 4:

Table 1 :

 1 Classification accuracy in LOO Cross-Validation

	Subject	SVM	SVM+ROS	MDRM [8]	ROS+MDRM
	1	77.27	79.28	64.3	84.67
	2	68.94	70.94	72.7	74.74
	3	62.46	62.93	63.3	60.72
	4	79.63	85.11	86.5	91.24
	5	67.06	70.11	74.2	76.11
	6	66.50	66.81	73.8	69.38
	7	71.77	78.89	79.9	88.60
	8	67.74	69.24	76.6	78.20
	9	76.09	74.73	79.6	86.19
	10	68.81	70.32	78.9	75.25
	11	72.47	73.98	59.9	72.62
	12	74.23	73.68	83.7	79.18
	13	68.62	73.28	73.4	81.95
	14	69.59	66.81	87.0	76.68
	15	68.62	72.20	87.0	81.72
	16	58.14	61.17	72.5	69.83
	Mean ±(std)	69.85 ± (5.5)	71.47 ± (6.32)	75.8 ± (8.3)	77.94 ± (7.84)

Acknowledgment

This research has been partially supported by the European project ERC-2012-AdG-320684-CHESS.


Florence Friebel
email: florence.friebel@institutoptique.fr

Alain Pellegrina

Dimitrios Papadopoulos

Patrice Camy

Jean-Louis Doualan

Richard Moncorge

Patrick Georges

Frédéric Druon

Dimitris N Papadopoulos

57-mJ 20-Hz multipass laser amplifier based on Yb:CaF 2 crystals

Keywords:

published or not. The documents may come

Introduction

High energy and high repetition rate (~100 Hz) solid state lasers have raised, for a few years now, an important interest and large European projects have been programed in this direction. Direct diode pumping appears to be the solution largely envisaged towards the development of such sources. This trend is due to the efficiency and the accessibility to high power and subsequently high repetition rate. Under these aspects 10-100-Hz multi-millijoule amplifiers based on Yb-doped materials have been studied and developed [4]. The characterisation of these amplifiers covers not only the energetic performance but also thermal issues. We are presenting in this paper a Yb:CaF 2 amplifier producing almost 60 mJ of energy based on a simple and stability-optimized design.

Experimental setup

For our experiments we desire certain characteristics from the gain medium: To amplify fs-laser pulses, we need a large emission bandwidth for the material in order to avoid gain narrowing which is for us typically around 4-nm. Additionally for high average power, we need good thermal conductivity. Usually a reference for the thermal conductivity the one of YAG is used; close to11 Wm -1 K -1 . On the other hand, to store the energy in the amplifier, a long fluorescence lifetime of the active medium is preferred. These characteristics fit for the Yb:CaF 2 crystal as gain medium (bandwidth=70nm, κ=9.7Wm -1 K -1 (undoped), lifetime=2.4ms) [1,[3][4][5]. But, the main drawback for an amplifier based on such a crystal, comes from a low emission cross-section: 0.25x10 -20 cm 2 [1,4]. To achieve a sufficient gain for a high-energy amplifier (typically a x50 gain for amplified pulses reaching the few tens of mJ), a special design of our multipass is suggested. Moreover, issues such as thermal lens management have also to be considered. The multipass cavity setup is shown in figure 1. The amplifier contains two crystals: 2 mm thick, 15 mm diameter and doped at 2.2%, in an active mirror configuration. The pump diode emits 400 W at 980 nm in 2.25ms pump in qcw operation, at 20Hz, delivering in total about 0.9 J. The pump beam is successively imaged to both Yb-CaF 2 crystals with a diameter of 1.3 mm. The signal beam comes from a regenerative amplifier based on Yb:KYW emitting 1.5 ns, 3.1-nm-bandwidth stretched pulses at 1kHz with energy of 1.1 mJ at 1030 nm (s-Pulse HP2, Amplitude Systems). The re-imaging multipass configuration shown in fig. 1 allows easily obtaining 9 bounds on each crystal. In order to double the number of passes, a re-injection configuration with a f=500mm lens, λ/4 and a mirror is added.

Energy performance

With this configuration the maximum output energy of the amplifier is around 57 mJ at 20 Hz. The output energy with increasing signal energy can be presented in figure 2. For a multipass amplifier with 18 passes the beam profile is excellent. M 2 -measurment revealed 1.1. The energy measurements are done at 20 Hz in order to decorrelate energy and power issues. During 30 min of operation at 50 mJ the beam remained stable with a pointing stability better than 20µrad rms.

Operation at 100 Hz

This stable operation encouraged us to increase the repetition rate up to 100 Hz. In order to avoid any thermal damages and beam distortions due to the increased heat load, thermal measurements are done. At first we investigated the surface temperature of the crystal with a thermal camera (FLIR Systems, Inc.) in the 8-12 µm range. The increase in temperature is only 15º C. In the active mirror configuration, the crystals are glued to a copper mount. This mount is set into a mount with water cooling from the backside.

Further, we investigated the behaviour of the thermal lens. Yb:CaF 2 is known to have a negative thermo-optic coefficient, χ=-11.3x10 -6 K -1 [2] leading to a negative thermal lens. Nevertheless, as presented in figure 4 we measured a positive thermal lens for the full range of incident pump power. This uncommon result is most probably linked to the active mirror configuration. It is possible that due to the differential deformation of to the two HR and AR coatings of the two sides, the crystal is thermo-mechanically bended to result in the observed focusing behaviour. Finally, we observed, for the first time to our best knowledge, the dynamic of this thermal lens (fig. 4). The main observation consists in a delay between the pumping and the maximum dioptre. This can be explained by a heat load linked to the fluorescence temporal evolution for this 3-level-laser configuration and not to the pumping pulse shape itself. This is corroborated by our simulations giving the temperature elevation versus time considering these two different temporal shapes as shown in figure 4.

Conclusion

We demonstrate a high energy multipass amplifier based on Yb:CaF 2 crystals delivering up to 57 mJ with a gain of 52 for 18 passes. The amplifier operated at 20 Hz. The operation has been stable at 50 mJ during 30 min with a pointing stability of ˂ 20μrad. The M 2 = 1.1 is excellent regardless the large number of passes. In order to extend the performances at 100 Hz thermal issues have been studied. The temperature elevation stays relatively low. The heat load increase on the surface is only 15º C. A positive thermal lens has been measured with a delayed dynamic evolution compared to the pump pulse. This thermal lens is low and can be compensated easily in our setup. The first point can be explained with mechanical deformation of the crystal in active mirror configuration; the second by the 3-level nature of Yb-lasers. The 100 Hz operation seems to be feasible since only minor thermal complications are expected in our configuration. Nevertheless, operating at 100 Hz is still under process due to beam pointing instability, due to some of our mount absorbing a part of the fluorescence, which creates air turbulences in the vicinity of the active medium.

Figure 1 :

 1 Figure 1: Multipass amplifier setup using 2 Yb-CaF2 active-mirror crystals. For clarity only 4 passes have been represented.

Fig. 2 .

 2 Fig. 2. The measurements are showing the output of the multipass amplifier at 18 passes with 20 Hz repetition rate. The maximum output is 57.4mJ. The Beam profile is displayed at the right side.

Fig. 3 .

 3 Fig.3. On the left side the thermal image of the crystal on a mount is visible. The blue line gives the cross-section for the temperature profile measurement. The result of that measurement is shown on the right side. The surface temperature is between 14 ºC on the Mount and 30 ºC in the middle of the pumping region.

Fig. 4 .

 4 Fig. 4. The image on the left side shows the evolving positive thermal lens with incident pump power. On the right side we see a finiteelement based simulation on the relation between fluorescence and thermal lens in the crystal.

Acknowledgments

This work has been partially funded by the ANR Femtocryble and the ILE-APOLLON 07-CPER 017-01.


Alexandre Hennequin
email: alexandre.hennequin@gipsa-lab.grenoble-inp.fr

Amélie Rochet-Capellan
email: amelie.rochet-capellan@gipsa-lab.grenoble-inp.fr

Marion Dohen
email: marion.dohen@gipsa-lab.grenoble-inp.fr

Auditory-visual Perception of VCVs Produced by People with Down Syndrome: Preliminary Results

Keywords: Down Syndrome, Speech perception, Multimodality, Intelligibility

Down Syndrome (DS) is a genetic disease involving a number of anatomical, physiological and cognitive impairments. More particularly it affects speech production abilities. This results in reduced intelligibility which has however only been evaluated auditorily. Yet, many studies have demonstrated that adding vision to audition helps perception of speech produced by people without impairments especially when it is degraded as is the case in noise. The present study aims at examining whether the visual information improves intelligibility of people with DS. 24 participants without DS were presented with VCV sequences (vowel-consonant-vowel) produced by four adults (2 with DS and 2 without DS). These stimuli were presented in noise in three modalities: auditory, auditoryvisual and visual. The results confirm a reduced auditory intelligibility of speakers with DS. They also show that, for the speakers involved in this study, visual intelligibility is equivalent to that of speakers without DS and compensates for the auditory intelligibility loss. An analysis of the perceptual errors shows that most of them involve confusions between consonants. These results put forward the crucial role of multimodality in the improvement of the intelligibility of people with DS.

Introduction

Down Syndrome (DS) is a genetic disease caused by the presence of a third chromosome 21. It is the first genetic cause of intellectual deficiency [START_REF] Katz | Intellectual disability: definition, etiological factors, classification, diagnosis, treatment and prognosis[END_REF]. Among others, it involves impairments in speech production which cannot be fully accounted for by the intellectual deficiency [START_REF] Kumin | Speech intelligibility and childhood verbal apraxia in children with Down syndrome[END_REF]- [START_REF] Kent | Speech Impairment in Down Syndrome: A Review[END_REF]. Phenotipic differences observed in people with DS, such as hearing impairments, muscle hypotonia, vocal tract abnormalities etc, also interfer with speech production [START_REF] Kent | Speech Impairment in Down Syndrome: A Review[END_REF], [START_REF] Martin | Language Characteristics of Individuals with Down Syndrome[END_REF]. All these specificities result in a lower intelligibility. This lack of intelligibility has however only been studied auditorily [START_REF] Kumin | Speech intelligibility and childhood verbal apraxia in children with Down syndrome[END_REF], [START_REF] Bunton | Phonetic intelligibility testing in adults with Down syndrome[END_REF]. On the other hand, a large body of research has shown that seeing someone without DS speak improves the perception of his/her speech, especially when it is deteriorated as is the case in a noisy environment [START_REF] Summerfield | Use of Visual Information for Phonetic Perception[END_REF], [START_REF] Grant | The use of visible speech cues for improving auditory detection of spoken sentences[END_REF]. This study therefore aims at evaluating whether or not adding the visual modality improves the intelligibility of people with DS. [START_REF] Kent | Speech Impairment in Down Syndrome: A Review[END_REF] published a review [START_REF] Kent | Speech Impairment in Down Syndrome: A Review[END_REF] of the research conducted on the speech of people with DS since the 50s. Despite discrepancies in the results, it appears that fundamental frequency (f0) is generally higher in the speech of people with DS than in that of controls. Vocal quality is also judged as breathy and rough. Acoustically, studies put forward increased perturbations and reduced SNR (Signal-to-Noise Ratio). People with DS tend to produce more articulatory and/or phonological errors [START_REF] Kumin | Speech intelligibility and childhood verbal apraxia in children with Down syndrome[END_REF], [START_REF] Bunton | Phonetic intelligibility testing in adults with Down syndrome[END_REF]. Acoustical analyses of vowel production in vowel-consonant-vowel (VCV) contexts suggest that people with DS display more variability in the first two formants (F1 and F2) and a higher F0 compared with typical speakers ( [START_REF] Rochet-Capellan | Acoustic characterisation of vowel production by young adults with Down syndrome[END_REF]; see also [START_REF] Kent | Speech Impairment in Down Syndrome: A Review[END_REF]). The production of speech sounds is disturbed by various anatomical specificities [START_REF] Kent | Speech Impairment in Down Syndrome: A Review[END_REF] : abnormal dentition (number and alignment), high palate, smaller oral cavity resulting in a relatively larger volume occupied by the tongue, etc. Motor control is also affected: generally, people with DS are described as hypotonic. A study on limb motion [START_REF] Latash | What is currently known about hypotonia, motor skill development, and physical activity in Down syndrome[END_REF] however suggests that rather than hypotonia, people with DS would rather display higher muscle activation thresholds: initiating movements, and more specifically those required to produce speech, may require more effort for people with DS.The speech of people with DS is therefore altered not only because of intellectual deficiency but by many other factors. This results in an observed lower intelligibility of people with DS, variable across individuals [START_REF] Kumin | Speech intelligibility and childhood verbal apraxia in children with Down syndrome[END_REF], [START_REF] Bunton | Phonetic intelligibility testing in adults with Down syndrome[END_REF]. Intelligibility is defined as "how well a speaker's acoustic signal can be accurately recovered by a listener" [START_REF] Hustad | The relationship between listener comprehension and intelligibility scores for speakers with dysarthria[END_REF]. Yet it is well known that the visual information helps perceive speech, and thus improves intelligibility, of typical speakers, especially in adverse conditions such as in noisy environments ( [START_REF] Summerfield | Use of Visual Information for Phonetic Perception[END_REF], [START_REF] Grant | The use of visible speech cues for improving auditory detection of spoken sentences[END_REF], [START_REF] Summerfield | Some preliminaries to a comprehensive account of audio-visual speech perception[END_REF] ; for a review, see [START_REF] Dohen | Speech through the ear, the eye, the mouth and the hand[END_REF]). For example, Grant & Seitz [START_REF] Grant | The use of visible speech cues for improving auditory detection of spoken sentences[END_REF] showed that seeing the face of a speaker producing sentences in noise improves the detection threshold of these sentences by 1.6 dB. Summerfield [START_REF] Summerfield | Some preliminaries to a comprehensive account of audio-visual speech perception[END_REF] put forward the fact that audition and vision are complementary in speech perception by examining confusions between English consonant in the auditory and visual modalities. It indeed appeared that mode of articulation is the most robust feature in the auditory modality whereas it is place of articulation in the visual modality. The speech produced by people with DS is acoustically degraded and displays a reduced SNR [START_REF] Kent | Speech Impairment in Down Syndrome: A Review[END_REF]. This raises the question whether adding the visual information would improve their intelligibility, as is the case for the speech produced by people without DS in noise. Considering the anatomical and motor specificities of speech production in DS, it remains unsure what their visual input consists in and how it is perceived. In the literature, speech production impairments in DS are often related to dysarthria [START_REF] Bunton | Phonetic intelligibility testing in adults with Down syndrome[END_REF]- [START_REF] Martin | Language Characteristics of Individuals with Down Syndrome[END_REF], [START_REF] Rochet-Capellan | Acoustic characterisation of vowel production by young adults with Down syndrome[END_REF]. Results in auditoryvisual (AV) perception of dysarthric speech could therefore provide valuable insight even if they should not prevail as granted for both populations. Hustad & Cahill [START_REF] Hustad | Effects of presentation mode and repeated familiarization on intelligibility of dysarthric speech[END_REF] examined the perception of low semantically predictable sentences produced by 5 speakers with dysarthria. Even if overall results show a greater intelligibility in the AV condition than in the auditory only condition, this difference is significant only for the speaker with the most severe dysarthria. A comparable study [START_REF] Keintz | Influence of visual information on the intelligibility of dysarthric speech[END_REF] investigated the perception of speech produced by 8 people with Parkinson's disease and dysarthria. The results show an improvement in intelligibility when vision is added to audition only for 3 out of 8 speakers, i.e. those with the lowest intelligibility scores in the auditory only condition. The present study aims at analyzing whether adding vision to audition can improve the intelligibility of speech produced by people with DS. The speech of 4 speakers (2 with DS, 2 without DS matched in gender and age) was presented in 3 modalities (Auditory Only, Video Only and Auditory-Visual) to listeners without DS, with little or no experience with this population. Meaningless VCV sequences were used to control for phonetic material and isolate pure segmental intelligibility from semantic context effects.

Method

Participants

24 native speakers of French without DS participated in this study (12 f -age: mean=25.1; se=3). None reported any uncorrected vision problems or any hearing or speech disorders or phonological issue. Before the experiment, their audition was positively tested with a pure-tone hearing screening at 30 dB for 500 Hz, 1 kHz, 2 kHz and 4 kHz bilaterally. At the end of the experiment, they received a 15€ gift card. All had little or no experience with people with DS.

Speakers and stimuli

4 native speakers were selected from a database recorded in a previous study (see [START_REF] Rochet-Capellan | Acoustic characterisation of vowel production by young adults with Down syndrome[END_REF]): 2 speakers without DS (a 22 year-old male and a 21 year-old female) and 2 speakers with DS (a 21 year-old male and a 19 year-old female). The speakers were matched in gender and approximate age. 9 expert participants performed an auditory perception pre-test without noise in order to individually evaluate the auditory intelligibility of the speakers with DS. From this test, we chose two speakers with a relatively good intelligibility for the present study: a too poor intelligibility coupled with the fact that stimuli were noised would have led to a floor effect.

The stimuli used consisted of 16 meaningless VCV sequences with V = /a/ and C

= {[b], [d], [g], [p], [t], [k], [f], [s], [ʃ], [v], [z], [ʒ], [l], [ʁ], [m],
[n]} covering the manners and places of articulation of French. Each VCV sequence was produced three times, and the clearest production (both auditorily and visuallly) was chosen as a stimulus for the present study.

The stimuli were recorded in a soundproof room. Speakers were seated in a chair in front of a loudspeaker, wore a head mounted microphone (Sennheiser HP4) and were filmed using a HD digital camera (Panasonic HC-X920). They were asked to repeat the VCV sequences they heard through the loudspeaker. Audio was sampled at 44100 Hz (Focusrite Scarlett 6i6 soundcard). Each audio file was normalized at 70 dB using Praat and noised (signal to noise ratio = -4 dB) with a "cocktail party" noise (BDBRUIT, [START_REF] Zeiliger | Bd_bruit, une base de données de parole de locuteurs soumis à du bruit[END_REF]). The files were then resynchronized with the videos using FFmpeg (https://www.ffmpeg.org/) at a 960x540 pixels resolution in three different versions: Auditory only (A, with the picture of a loudspeaker), Video only (V) and Auditory-Visual (AV) resulting in a total of 192 stimuli: 4 speakers x 3 modalities x 16 VCV sequences.

Procedure

Participants were seated approximately at 60 cm from a 24" screen and wore a headset (Audio Technica BPHS1). The experience was programmed using the Psychophysics Toolbox [START_REF] Brainard | The Psychophysics Toolbox[END_REF]- [START_REF] Kleiner | What's new in Psychtoolbox-3?[END_REF]. Videos were presented at the center of the screen. The test was divided into three blocks, one for each modality (A, V and AV), consisting of 64 stimuli each (16 VCV x 4 speakers). Orders of blocks and stimuli within each block were randomized. Participants were informed that they would either hear/ or see or hear and see a stimulus presented twice in a row. Their task was then to repeat what they had understood. They then hit a key on the keyboard to move to the next stimulus. Audio was sampled at 48 kHz (Focusrite Scarlett 6i6 soundcard). They were told that the stimuli were meaningless speech sequences. No other information on the structure of the sequences was provided. The test was preceded by a training phase using noiseless stimuli different from those of the experiment. Training consisted of 2 stimuli per block. The order of presentation of the blocks was not necessarily the same in the training and the actual experience. At the end of this training, participants listened to a brief sample of the "cocktail party" noise and were informed that the stimuli from the actual experiment were all mixed with this type of noise.

Response transcription and analyses

The responses provided by the participants were transcribed using the following code: BeforeV1-V1-C-V2-AfterV2. Each part was phonetically transcribed or left empty (e.g., "brata" instead of "ata": beforeV1='br' -V1='a' -C='t' -V2='a' -AfterV2=''). An unperceived consonant was transcribed 'h'. If the response was only a vowel (e.g., 'a' instead of 'ata'), it was transcribed as V2 (V1='' -C = 'h' -V2='a'). Responses that could not be transcribed were coded '?' (BeforeV1=V1=C=V2=AfterV2='?').

Results were analyzed using the R software (R Development Core Team, 2008) and analyses of variance (aov function with default parameters). Post-Hoc comparisons (Student tests) were corrected using the Bonferroni correction.

Confusion trees were built to examine confusions between consonants in the visual and auditory modalities separately. First confusion matrices were computed for each speaker group : each cell (m i , n j ) contains the number of times the consonant m i was perceived as n j . These matrices were then used to compute Euclidian distance matrices which were in turn fed to a divisive hierarchical clustering algorithm (diana function in the package cluster from R -[19]). The resulting data was then plotted as a dendogram.

Results

A correct response corresponds to the case in which V1, C and V2 were correctly identified and BeforeV1='' and AfterV2=''. Global analyses show that 44.2% of the responses were correct, and 54.4% contained at least one error. The remaining 1.4% could not be transcribed. Speaker group and modality do not have an effect on these percentages (p > 0.1). Figure 1 shows the percentages of correct responses depending on speaker group and modality. We conducted an ANOVA on these percentages with two within-subject factors (speaker group and modality) and one between-subject factor (order of presentation of modalities). Modality has a significant effect (F(2,36)=263.5 -p < 0.001) : there are more correct responses in the AV modality than in A (A vs. AV: t(23)=-12.1 ; p < 0.001) than in V (A vs. V: t(23)=5.5 p < 0.001). Overall, results are better for speakers without DS than speakers with DS (F(1,18)=14.6 -p = 0.001). This however depends on the modality (speaker group * modality: F(2,36) = 13.6 -p < 0.001) : in the A modality, speakers without DS are better perceived than those with DS (t(23) = 6.7 -p < 0.001) but this is not the case in the V modality (t(23) = -0.9 -p > 0.9). In the AV modality, there is only a trend towards significance (significant before correction) for speakers without DS to be better perceived than those with DS (t(23)=2,1 -p > 0.1). The order of presentation also has a significant effect (F(5,18)=3,2 -p < 0.05) and interacts with modality (F(10,36)=3,2 -p < 0.01). This effect is significant only in the V modality: when the AV modality was presented before V, the results in V are significantly better.

Correct responses

Errors

General analysis -Errors were divided into three categories: insertions before and/or after the VCV sequence (beforeV1≠'' and/or afterV2≠''), errors on vowels (V1 and/or V2) and error on the consonant. These three categories can co-occur in the same response. Figure 2 shows the repartition of the errors depending on error type. More than 80% of the errors (response contains one or more errors) occur on the consonant (Figure 2). This is the reason why only errors on the consonant were analyzed into detail.

Errors on the consonant -The consonant (C) responses were divided into three categories: correct, confusion with another consonant and other (e.g., addition of one or more consonants). An ANOVA was conducted on this data with three within-subject factors: speaker group, modality and error type. Note that 94.5% of the responses are either correct responses or confusions with another consonant.

Confusion with another consonant is the most frequent type of error (F(1,23) = 228.3 -p < 0.001). Errors on the consonant occur more often in A and V modalities than in AV (F(2,46) = 206.4 -p < 0.001). Overall, there is no difference between speaker groups (F(1,23) = 2.4 -p > 0.1). There are however more errors in the A modality for speakers with DS than for speakers without DS (speaker group * modality: F(2,46) = 3.6 -p < 0.05). In order to further analyze confusions between consonants, we used the same type of representation as Summerfield [START_REF] Summerfield | Some preliminaries to a comprehensive account of audio-visual speech perception[END_REF]. Confusions are presented as a tree in which each "leaf" corresponds to a consonant. The closer the consonants are in the tree, the more often they are confused. Figure 3 presents the confusion trees depending on modality (A vs. V) and speaker group (without vs. with DS). The colors used in the trees for the V modality correspond to a grouping of consonants by place of articulation (1 color for each place of articulation) and those in the tress for the A modality to a grouping by manner of articulation (voiced vs. unvoiced). Figure 3, shows that consonants are grouped by color (manner of articulation) for speakers without DS but not for those with DS. Manner of articulation is thus a robust feature in the A modality for speakers without DS but not for those with DS. In the V modality, consonants are mainly grouped by place of articulation (consonants with the same color are grouped) in both speaker groups. The only exception is for velars for speakers without DS and for velars and alveolars for speakers with DS. The place of articulation therefore appears to be a robust feature in the V modality for both groups of speakers.

Discussion

This study examined the perception of VCV sequences produced by speakers with and without DS by participants without DS in three modalities: auditory (A), visual (V) and auditory-visual (AV). The sequences were presented in a cocktail-party noise. The aim of this study was to question whether adding the V modality could improve the intelligibility of speech produced by speakers with DS as it does for speech produced by speakers without DS. Overall, the results show that adding the visual modality improves the perception of noisy speech (better results in the AV modality than in the A and V modalities) whichever the group. The percentage of correct responses are lower for speakers with DS than for those without DS in the A modality. This confirms previous results ( [START_REF] Kumin | Speech intelligibility and childhood verbal apraxia in children with Down syndrome[END_REF], [START_REF] Bunton | Phonetic intelligibility testing in adults with Down syndrome[END_REF]): in the A modality, speech produced by our two speakers with DS is less intelligible than that produced by speakers without DS. The difference in intelligibility between the two groups of speakers is much smaller in the AV modality (not even significant after correction for multiple comparison). This suggests that adding the visual modality at least partly compensates for the lack of auditory intelligibility of speech produced by our two speakers with DS. There is no difference in the percentages of correct responses between the two groups in the V modality: our two speakers with DS are visually as intelligible as those without DS. Note however that when the V modality is presented before the AV modality in the experimental procedure, the results are significantly lower than when it is presented after the AV modality for both speaker groups. This presentation order effect could be explained by the fact that, since it is easier to perceive speech in the AV modality, doing it before perceiving it in the V modality trains the participants and improves their perception in the V modality. It is also possible that participants memorize the auditory-visual association of a given stimulus, and that, when they encounter it later in the experiment in V modality, it is easier for them to recover the correct response. For dysarthric speech, an improvement in intelligibility by adding the V modality was observed only for speakers with the most severe dysarthria [START_REF] Hustad | Effects of presentation mode and repeated familiarization on intelligibility of dysarthric speech[END_REF], [START_REF] Keintz | Influence of visual information on the intelligibility of dysarthric speech[END_REF]. In this study we found such an improvement for our two speakers with DS with a relatively good level of intelligibility (see 2.2 for more information). It would therefore be interesting to explore whether the improvement is even larger for speakers who are less intelligible. Over all speaker groups, the most frequent type of error was confusion between consonants. Note that the consonant was the only phoneme of the sequence that varied in the experiment (V = /a/). Further analysis of the types of confusions made in the A and V modalities (confusion trees) confirmed that, for speakers without DS, the most robust feature in noise is the manner of articulation in the A modality and the place of articulation in the V modality (same result as in [START_REF] Summerfield | Some preliminaries to a comprehensive account of audio-visual speech perception[END_REF]). Our results show that the robustness of place of articulation in V perception is relatively well preserved in the speech produced by people with DS. Robustness of manner of articulation in A perception is however altered in the speech of people with DS. This suggests that voicing is a feature especially difficult to produce by people with DS as already suggested in [START_REF] Rochet-Capellan | Acoustic characterisation of vowel production by young adults with Down syndrome[END_REF]. More detailed analyses will have to be conducted to examine the ability to detect place and manner of articulation in the speech of people with DS compared to that of people without DS. Note that this study used only one vowel. We indeed decided to focus on the perception of consonants in four speakers and adding a variation of the vowel would have resulted in a too long experiment. It would however be interesting to examine whether adding the V modality also improves the perception of vowels produced by people with DS especially since we know that they are acoustically different from those produced by speakers without DS [START_REF] Rochet-Capellan | Acoustic characterisation of vowel production by young adults with Down syndrome[END_REF].

Acknowledgements

Figure 1 :

 1 Figure 1: Percentages of correct responses depending on speaker group (without vs. with DS) and modality (AV, A, V)

Figure 2 :

 2 Figure 2: Distribution of errors depending on location.

  The research leading to these results has received funding from the European Research Council under the European Community's Seventh Framework Programme (FP7/2007-2013 Grant Agreement no.339152-"Speech Unit(e)s"). This work is linked to the project "Communiquons Ensemble" (Communicate Together) funded by the Fondation Internationale de la Recherche Appliquée sur le Handicap (FIRAH). The authors want to thank the participants, the Association de Recherche et d'Insertion Sociale des Trisomiques (ARIST) and the ARIST professionals of the ESAT-SAJ.

Figure 3 :

 3 Figure 3: Consonant confusion trees depending on speaker group (without DS and with DS) and modality (Visual and Auditory). The colors in the trees for the V modality correspond to grouping of consonants by place of articulation (red=bilabial -green=labiodental -bleu=dental -grey=alveolar -orange=post-alveolar -pink=velar -yellow=uvular) and those in the trees for the A modality to a grouping by manner of articulation (red = voiced -green=unvoiced). N.B.: S=[ʃ] -Z=[ʒ] -R=[ʁ].


F O Grodji

Vafi Doumbia
email: vafid@yahoo.fr

K Boka

C Amory-Mazaudier

Y Cohen

R Fleury

Estimating some parameters of the equatorial ionosphere electrodynamics from ionosonde data in West Africa

Keywords: Equatorial Ionosphere, Equatorial electrojet, IPS-42 ionosonde, Electric fields and currents

During the International Equatorial Electrojet Year (IEEY), an IPS-42 ionosonde located at Korhogo (9.33°N, 5.42°W, -1.88°dip-lat) and a meridian chain of 10 magnetic stations were setup in West Africa (5°West longitude). In this work, some characteristic parameters of the equatorial electrojet were estimated on the basis of the IPS-42 ionosonde data at Korhogo during the years 1993 and 1994. The study consisted of determining the zonal electric field through an estimate of the plasma vertical drift velocity. The daytime plasma vertical drift velocity was estimated from the time rates of change of the F-layer virtual height variations and a correction term that takes into account the ionization production and recombination effects. This method resulted in an improved vertical drift velocity, which was found to be comparable to the results of previous studies. The estimated vertical drift velocity was used in a semi-empirical approach which involved the IRI-2012 model for the Pedersen and Hall conductivities and the IGRF-10 model for the geomagnetic main field intensity. Thus the zonal and polarization electric fields on one hand, and the eastward Pedersen, Hall and the equatorial electrojet current densities on the other hand, were estimated. Furthermore the integrated peak current density at the EEJ center was estimated from ionosonde observations and compared with that inferred from magnetometer data. The integrated EEJ peak current densities obtained from both experiments were found to be in the same order and their seasonal variations exhibit the same trends as well.

Introduction

At the geomagnetic dip-equator, the orthogonally crossed eastward electric field and northward geomagnetic field combine with the differential motions between ions and electrons in the E-region of ionosphere, to produce a strong vertical polarization electric field. This electric field associates with the northward geomagnetic field to increase the east-west electrical conductivity along the geomagnetic dip-equator in a narrow latitude band of ±3 degrees [START_REF] Cowling | The electrical conductivity of an ionized gas in the presence of a magnetic field[END_REF][START_REF] Martyn | Electric conductivity of the ionospheric D-region[END_REF][START_REF] Baker | Electric current in the ionosphere, I-The conductivity[END_REF][START_REF] Baker | Electric current in the ionosphere, I-The conductivity[END_REF][START_REF] Sugiura | A model equatorial electrojet[END_REF]Cain, 1966). This process setup an intense eastward current, known as "equatorial electrojet" [START_REF] Chapman | The equatorial electrojet as detected from the abnormal electric current distribution above Huancayo, Peru and Elsewhere[END_REF] along the geomagnetic dip equator. In addition, occurrences of phenomena like equatorial spread F, plasma bubbles and diverse plasma density irregularities, which disturb radio waves propagation near the dip-equator, are associated with this special characteristic of the equatorial ionosphere.

Due to the EEJ current flow, the daily regular variations of the geomagnetic field horizontal component (H) are enhanced by a ratio of 2 to 2.5 near the dip-equator [START_REF] Bartels | Some features of the large geomagnetic tides in the horizontal force at Huancayo[END_REF][START_REF] Fambitakoye | The equatorial electrojet and regular daily variation S R : I. A determination of the equatorial electrojet parameters[END_REF], Doumouya et al., 1998). Thus most of the spatial and temporal characteristics of the EEJ (latitude, longitude and height dependence; local time, day to day and seasonal variability, as well as the dependence on solar cycle) have been evidenced from its magnetic effects. Those effects were estimated from ground-based magnetic observations [START_REF] Forbush | The Equatorial electrojet in Peru[END_REF][START_REF] Onwumechili | Geomagnetic variation in the equatorial zone, physics of Geomagnetic phenomena-I[END_REF][START_REF] Fambitakoye | The equatorial electrojet and regular daily variation S R : I. A determination of the equatorial electrojet parameters[END_REF][START_REF] Hesse | An investigation of the equatorial electrojet by mean of ground-based magnetic measurements in Brazil[END_REF]Doumouya andal, 1998, 2003); as well as from rockets [START_REF] Sampath | Results from "in situ" measurements of ionosphere currents in the equatorial zone[END_REF] and polar-orbiting satellites observations [START_REF] Cain | The POGO data[END_REF][START_REF] Onwumechili | Longitude variation of equatorial parameters derived from POGO satellite observations[END_REF][START_REF] Jadhav | A Detailed study of equatorial electrojet phenomenon using ∅rsted satellite observations[END_REF][START_REF] Doumouya | Improving and testing the empirical equatorial electrojet model with CHAMP satellite data[END_REF][START_REF] Lühr | Noon-time equatorial electrojet: Its spatial features as determined by the CHAMP satellite[END_REF][START_REF] Mouel | The field of the equatorial electrojet from CHAMP data[END_REF][START_REF] Alken | Spatio-temporal characterization of the equatorial électrojet from CHAMP, ∅rsted, SAC-C satellite magnetic measurements[END_REF]. In particular, the EEJ width, thickness, position of its center and especially its peak current density, known as the EEJ parameters, are usually inferred from its magnetic effects [START_REF] Onwumechili | Geomagnetic variation in the equatorial zone, physics of Geomagnetic phenomena-I[END_REF][START_REF] Fambitakoye | The equatorial electrojet and regular daily variation S R : I. A determination of the equatorial electrojet parameters[END_REF][START_REF] Doumouya | The equatorial électrojet at African Longitudes: First result from magnetic measurement[END_REF][START_REF] Rabiu | Characteristics of equatorial electrojet over India determined from a thick current shell model[END_REF]. In addition, [START_REF] Anghel | Estimating day-time vertical ExB drift velocities in the equatorial F-region using ground-based magnetometer observations[END_REF]2004 and2006) proposed an empirical method to determine the equatorial F-region plasma vertical drift velocity from the EEJ magnetic effects. This method consists of using an estimate of the EEJ contribution )ܪ∆( in the daily variations of the geomagnetic field horizontal component .)ܪ( However, most parameters of the equatorial electrodynamics cannot be reliably estimated from magnetic data alone. Among these parameters, the zonal electric field ܧ( ሬԦ ௬ ), the vertical polarization electric field ܧ( ሬԦ ), the eastward Pedersen ܬ( Ԧ ଵ ) and Hall current ܬ( Ԧ ுଶ ) densities and the net eastward EEJ current density ܬ( Ԧ ாா ) can be mentioned.

At the dip-equator, the zonal electric field and the northward geomagnetic field combine to produce the F-region plasma vertical drift. The zonal electric field can be approximately estimated if the F-region plasma vertical drift velocity and the geomagnetic main field intensity are known. While the geomagnetic field intensity can be easily estimated at any location through accurate models like IGRF, the F-region plasma vertical drift velocity, on the contrary, is harder to get everywhere. In fact satellite measurements provided the global view of equatorial F-region plasma drifts and associated electric field (Maynard et al., 1988;[START_REF] Coley | Low-latitude zonal and vertical ion drifts seen by DE2[END_REF][START_REF] Coley | Equatorial fountain effect and dynamo drift signatures from AE-E observations[END_REF][START_REF] Heelis | East-west drifts at midlatitudes observed by dynamics explorer 2[END_REF]. Those measurements depicted the longitudinal, seasonal and solar cycle effects (see Fejer et al., 1995 and references therein). In addition, regional climatology models of the equatorial Fregion plasma drift velocity were developed in the Peruvian, Brazilian and Indian longitude sectors [START_REF] Scherliess | Radar and satellite global equatorial F-region vertical drift model[END_REF]. [START_REF] Richmond | An empirical model of quiet-day ionospheric electric fields at middle and low latitudes[END_REF] and Fejer (1999) reported as well on global empirical models of magnetically quiet time equatorial F-region vertical drift velocity.

Other studies of the equatorial F-region plasma vertical drifts were performed using various techniques of measurements. For example, Ionosondes and HF Doppler radars have been used to study the equatorial F-region vertical drifts [START_REF] Namboothiri | Vertical plasma drifts in the F-region at magnetic equator[END_REF][START_REF] Goel | Post-sunset rise of F-layer height in the equatorial region and its relation to the F-layer dynamo polarization fields[END_REF][START_REF] Murthy | Night-time equatorial thermospheric meridional winds from ionospheric h'F data[END_REF]Hari andKrishna Murthy, 1995, Blanc and[START_REF] Blanc | Typical disturbances of the daytime equatorial F region observed with a high-resolution HF radar[END_REF]. The most reliable measurements of the F-region plasma vertical drift velocity near the geomagnetic dip-equator were performed by Incoherent Scatter Radar at Jicamarca [START_REF] Woodman | Vertical drift velocities and east-west electric field at the magnetic equator[END_REF][START_REF] Farley | Equatorial spread F: Implication of VHF radar observation[END_REF][START_REF] Fejer | Average vertical and zonal Fregion plasma drifts over Jicamarca[END_REF]. However, such reliable measurements of the equatorial F-region plasma vertical drift are not available everywhere. In the African longitude sector, only ionosonde data can be used for such purpose (Iheonu and Oyekola, 2005;[START_REF] Oyekola | Morphology of F-region vertical ܧ × ܤ drifts in the African sector using ionosonde measurements[END_REF]. However, Woodman et al. (2006) and Bertoni et al. (2006) compared the rate of F-layer height variations (

ௗ ᇲ ி ௗ௧
) from digisonde data with vertical drift inferred from Jicamarca Incoherent Scatter Radar data. A fairly good agreement was found between digisonde (

ௗ ᇲ ி ௗ௧
) and incoherent scatter radar results during Pre-reversal Enhancement, when electric convection effects are significantly dominant over recombination and production effects (Woodman et al., 2006). [START_REF] Redmon | A Forecasting Ionospheric Real-time Scintillation Tool (FIRST)[END_REF] also found a quasi perfect linear correlation between the h'F and the vertical drift velocity during the Pre Reversal Enhancement at Jicamarca. For the rest of the time, when production and recombination are important, Woodman et al. (2006) found that digisonde (

ௗ ᇲ ி ௗ௧
) does not accurately represent the real F-region vertical drift. However, they assumed that digisonde derived F-region vertical drift could be improved by taking into account the production and recombination effects. Iheonu and Oyekola (2005) and [START_REF] Oyekola | Morphology of F-region vertical ܧ × ܤ drifts in the African sector using ionosonde measurements[END_REF] considered the production and recombination effects to estimate the daytime plasma vertical drift velocity.

In this work, a comparative study based on the IPS-42 ionosonde data and the magnetic data is carried out. The plasma vertical drift velocity (ܸ ௗ ) is estimated on the basis of the IPS-42 ionosonde data recorded at Korhogo [START_REF] Vila | Fabry-Perot interferometer measurements of neutral winds and F2 layer variations at the magnetic equator[END_REF] during the IEEY campaign. Based on the subsequent plasma vertical drift velocity, an attempt of estimating the zonal electric field ܧ( ሬԦ ௬ ), the vertical polarization electric field ܧ( ሬԦ ), the eastward Pedersen ܬ( Ԧ ଵ ) and Hall current ܬ( Ԧ ுଶ ) densities and the net eastward current density ܬ( Ԧ ாா ) will be made.

In addition the integrated peak current density ܫ( ) at the EEJ center will be estimated by integrating the net eastward EEJ current density ܬ( Ԧ ாா ) in height. The results of the integrated peak current density inferred from ionosonde data ܫ( ) will be compared with that obtained from ground-based magnetic data ܫ( ) in West Africa.

Basic equations

Figure 1 schematically summarizes in 3 steps the processes that lead to the equatorial electrojet current flow [START_REF] Martyn | Electric conductivity of the ionospheric D-region[END_REF][START_REF] Baker | Electric current in the ionosphere, I-The conductivity[END_REF][START_REF] Baker | Electric current in the ionosphere, I-The conductivity[END_REF].

Step 1:

In the dynamo region of the ionosphere near the dip-equator, the horizontal northward geomagnetic field ܤ ሬԦ and zonal electric field ܧ ௬ ሬሬሬሬԦ , produce an eastward Pedersen current ܬ ଵ ሬሬሬሬሬԦ (Eq. 1), and a vertical downward Hall current ܬ ுଵ ሬሬሬሬሬԦ (Eq. 2) associated with electrons upward vertical ܧ ሬԦ × ܤ ሬԦ drift.

ܬ ଵ ሬሬሬሬሬԦ = ߪ ܧ ௬ ሬሬሬሬԦ Eq. ( 1)

ܬ ுଵ ሬሬሬሬሬԦ = -ߪ ு ( ா ሬሬሬሬሬԦ × ሬԦ ) Eq. (2)
ߪ and ߪ ு are respectively Pedersen and Hall conductivities.

Step 2: On one hand, as ions ܧ ሬԦ × ܤ ሬԦ drift is impeded in the E-region due to collisions with neutral particles while electrons are relatively free to move, the resulting charge separation gives rise to an upward vertical polarization electric field ܧ( ሬሬሬሬԦ ). On the other hand, ܧ ሬሬሬሬԦ gives rise to an upward vertical Pedersen current ܬ ଶ ሬሬሬሬሬԦ (Eq. 3):

ܬ ଶ ሬሬሬሬሬԦ = ߪ ܧ ሬሬሬሬԦ Eq. (3)
And the ܧ ሬሬሬሬԦ × ܤ ሬԦ westward electron drift gives rise to an intense eastward Hall current ܬ ுଶ ሬሬሬሬሬԦ (Eq. 4):

ܬ ுଶ ሬሬሬሬሬԦ = -ߪ ு ( ா ሬሬሬሬሬԦ × ሬԦ )
Eq. ( 4)

Step 3:

When the polarization process is complete, the upward vertical Pedersen current ܬ ଶ ሬሬሬሬሬԦ counterbalances the downward Hall current ܬ ுଵ ሬሬሬሬሬԦ (Figure 1), then the net vertical current becomes nil (Eq.5 and Eq.6):

ܬ ௭ ሬሬԦ = ܬ ுଵ ሬሬሬሬሬԦ + ܬ ଶ ሬሬሬሬሬԦ = 0
Eq. ( 5)

ܬ ௭ ሬሬԦ = ߪ ܧ ሬሬሬሬԦ -ߪ ு ൬ ா ሬሬሬሬሬԦ × ሬԦ ൰ = 0
Eq. ( 6)

The eastward Hall current ܬ ுଶ ሬሬሬሬሬԦ superimposes the primary eastward Pedersen current ܬ ଵ ሬሬሬሬሬԦ . Thus the total eastward current density is:

ܬ ாா ሬሬሬሬሬሬሬԦ = ܬ ଵ ሬሬሬሬሬԦ + ܬ ுଶ ሬሬሬሬሬԦ = ߪ ܧ ௬ ሬሬሬሬԦ -ߪ ு ( ா ሬሬሬሬሬԦ × ሬԦ )
Eq. ( 7)

From Eq. ( 6) the vertical polarization electric field can be expressed by Eq. ( 8):

ܧ ሬሬሬሬԦ = ఙ ಹ ఙ ൬ ா ሬሬሬሬሬԦ × ሬԦ ൰ Eq. (8)
Replacing ܧ ሬሬሬሬԦ in Eq. ( 7), the equatorial electrojet net current density can be expressed as:

ܬ ாா ሬሬሬሬሬሬሬԦ = (ߪ + ఙ ಹ మ ఙ ܧ) ௬ ሬሬሬሬԦ Eq. ( 9
)
Where

ߪ = ߪ + ఙ ಹ మ ఙ
is the net eastward conductivity known as "Cowling conductivity".

The polarization electric field ܧ ሬሬሬሬԦ and the EEJ current density ܬ ாா ሬሬሬሬሬሬሬԦ can be estimated respectively through Eq. ( 8) and Eq. ( 9), if the zonal electric field ܧ ௬ ሬሬሬሬԦ , the geomagnetic field intensity ,ܤ the Pedersen conductivity ߪ and the Hall conductivity ߪ ு are known. In this work, we used the Pedersen and Hall conductivities integrated along the geomagnetic field lines. The integrated Pedersen (∑ ) and Hall (∑ ு ) conductivities are estimated through the local conductivities that are determined from the IRI-2012 model. The geomagnetic field intensity )ܤ( is estimated from the IGRF-10 model. The zonal electric field ܧ( ௬ ሬሬሬሬԦ ) is determined through Eq. ( 10) from the plasma vertical drift velocity (ܸ ሬԦ ௗ ) that will be estimated from the IPS-42 ionosonde data at Korhogo.

ܸ ሬԦ ௗ = ா ሬሬሬሬሬԦ × ሬԦ మ
Eq. ( 10)

Datasets and data processing

During the International Equatorial Electrojet Year (IEEY), many different instruments were deployed in West Africa from 1992 to 1995 [START_REF] Amory-Mazaudier | International Equatorial Electrojet Year[END_REF]. The campaign involved a network of three ionosondes, a Fabry-Perrot interferometer [START_REF] Vila | Fabry-Perot interferometer measurements of neutral winds and F2 layer variations at the magnetic equator[END_REF] and an HF radar [START_REF] Blanc | Typical disturbances of the daytime equatorial F region observed with a high-resolution HF radar[END_REF]. A meridian chain of ten magnetic stations was deployed across the geomagnetic dip-equator, from -6.30° to +6.76° dip-latitudes [START_REF] Doumouya | The equatorial électrojet at African Longitudes: First result from magnetic measurement[END_REF][START_REF] Vassal | A study of transient variations in the earth's electromagnetic field at equatorial electrojet latitudes in western Africa (Mali and Ivory Coast)[END_REF]. Figure 2 shows the ionosonde location and the magnetometer network. The geographic coordinates of the stations are given in Table 1. At that occasion, variations of the geomagnetic field and various parameters of low-latitude ionosphere have been monitored in view of deepening our knowledge on equatorial and low latitude electromagnetic phenomena and underlying physical processes.

The purpose of the present work is using the IPS-42 ionosonde data and the magnetometer data for a comparative study of the equatorial electrojet parameters.

The IPS-42 ionosonde data

The IPS-42 ionosonde equipments includes an IPS-42 sounder that operates in the frequency range of 1 to 22.6 MHz, with an emission power of 5 kW; a delta type antenna oriented in the North-South direction for emission and East-West for reception; and finally a DBD which is a numerical device designed for IPS-42 sounder data processing. These equipments have operated at Korhogo (5.43°W, 9.34°N, -1.88° dip-lat) from November 1992 to December 1998 [START_REF] Vila | Fabry-Perot interferometer measurements of neutral winds and F2 layer variations at the magnetic equator[END_REF].

The ionosonde data are sampled by 15 minute time intervals. The data are recorded in form of ionograms. The ionogram exploitation provides the characteristic parameters of the layers of ionosphere, which are respectively their virtual heights (h'E, h'F1, h'F2) and their critical frequencies (f oE , f oF1 and f oF2 ). In this study we use SAO explorer (http://www.ulcar.uml.edu) to analyze the IPS-42 ionosonde data. Note that the SAO explorer is an empirical model, which is mostly used for digisonde data analysis [START_REF] Abdu | Equatorial Spread F and Ionization Anomaly development as diagnosed from conjugate point observation (COPEX) in Brasil[END_REF]Reinish et al., 2004;Woodman et al., 2006). For the IPS-42 data analysis, the ionograms have been first scaled manually and converted into digisonde data format by using the NHPC software. Then, the converted data can be processed with the SAO explorer to obtain the virtual height of F-layer (h'F), the F2 layer critical frequency (foF2), the F2 layer peak height (hmF2), the Thickness parameter (Bo), the shape parameter (B1) and the plasma scale height (H).

For this study, ionograms of geomagnetic quiet days were selected according to the daily mean values of the geomagnetic activity index ݉ܣ considered to be lower than 20 nT [START_REF] Doumouya | The equatorial électrojet at African Longitudes: First result from magnetic measurement[END_REF]. In geomagnetic quiet time conditions, 53 days in 1993 and 39 days in 1994, thus a total of 92 days were selected. This evening brisk variation of the ℎ ᇱ ܨ corresponds to the Pre-Reversal Enhancement (PRE)

of the ionospheric zonal electric field (Kelley et al., 2009).

In order to estimate the F-region daytime plasma vertical drift velocity ܸ ௗ , we first consider the apparent velocity (ܸ') to which a correction term ܸ is added to account for ionization production )ݍ( and recombination loss coefficient (ߚܰ). The apparent drift velocity (ܸ') corresponds to the rate of the diurnal variations of the virtual height ℎ ᇱ :ܨ

ܸ' = ௗ ᇲ ி ௗ௧
Eq. ( 11)

The correction term ܸ is obtained through equation ( 12) as:

ܸ = ு• ே -ߚ • ܪ Eq. ( 12
)
(Iheonu and Oyekola, 2005;[START_REF] Oyekola | Morphology of F-region vertical ܧ × ܤ drifts in the African sector using ionosonde measurements[END_REF] Where ܪ = (ܰ ିଵ ௗே ௗ ) ିଵ is the ionization scale height;

,߯(ݍ ℎ) = ݍ , exp (1 -ℎ -.߯ܿ݁ݏ exp(-ℎ))
is ionization production rate according to Chapman formula.

ߚ is the attachment coefficient calculated using MSIS-E-90 models [START_REF] Hedin | MSIS-87 thermospheric model[END_REF].

ܰ = 2ܨ݉ܰ × ୣ୶୮ (ିఞ ಳభ )
ୡ୭ୱ୦ ఞ , with 2ܨ݉ܰ = 1.24 × 10 ଵ )2ܨ݂( ଶ , the maximal density and

߯ = ிଶି బ
, the zenithal angle.

Due to the small dip-latitude of Korhogo (-1.88°dip-lat.) the contributions of the plasma diffusion along the field lines to the F-region daytime vertical drift velocity ܸ ௗ are very small in comparison with the ionization and recombination effects. Thus the diffusion term )ܦ( can be neglected (Iheonu and Oyekola, 2005).

Finally, the daytime vertical drift velocity ܸ ௗ is determined according to the following relationship:

ܸ ௗ = ∆ ᇲ ி ∆௧ + ܸ
Eq.( 13)

ܸ ௗ = ∆ ᇲ ி ∆௧ + ு• ே -ߚ • ܪ Eq.( 14
)
Where ∆ℎ ᇱ ܨ is the F-region virtual height variation over the time interval ݐ∆ = 15݉݅݊.

Bittencourt and Abdu (1981) showed that, after sunset (q=0), the apparent F layer vertical drift velocity (

∆ ᇲ ி ∆௧
) inferred from ionosonde measurements represents the true vertical drift velocity above 300 km. However, below 300 km the apparent vertical velocity significantly departs from the true vertical drift velocity due to the increasing dominant recombination process at lower altitudes. Those results were also confirmed by Krishna [START_REF] Murthy | Night-time equatorial thermospheric meridional winds from ionospheric h'F data[END_REF]. This remark was taken into account for the night time drift velocity estimation.

From the F-region daytime vertical drift velocity the zonal electric field can be determined according to Eq. (10). At the magnetic equator, the zonal electric field ܧ( ௬ ሬሬሬሬԦ ) and the geomagnetic field ܤ( ሬԦ ) are both horizontal and perpendicular. Therefore the Plasma vertical drift velocity in the F-region can be expressed as:

ܸ ௗ = ா Eq. ( 15
)
From Eq. 15, ܧ ௬ is determined by: 16)

ܧ ௬ = ܤ • ܸ ௗ Eq. (
The values of the geomagnetic field B are given by the International Geomagnetic Reference

Field IGRF-10 model [START_REF] Macmillan | Ninth generation International Geomagnetic Reference Field Released[END_REF] from the geomagnetic field calculator of website (http://www.ngdc.noaa.gov/geomag-web/#igrfwmm). For the station of Korhogo, ܤ = 30392 ݊ܶ according to the IGRF-10 model for the epoch 1993.5.

Note that the Eq. ( 16) can be obtained at the magnetic dip-equator (inclination I=0) from the relationship established by [START_REF] Balsley | Electric field in the equatorial ionosphere: a review techniques and measurements[END_REF], in which the zonal electric field is expressed as function of the electrons vertical drift velocity, of the geomagnetic field intensity and inclination:

ܧ ௬ = .ܤ ܸ ௭ . cos ܫ Eq. ( 17)

ܸ ௭ = ܸ ௗ
തതത is the average of the electrons vertical drift velocity.

The polarization electric field is estimated based on Eq. ( 8). At the dip equator, the zonal electric field ܧ( ௬ ሬሬሬሬԦ ) is perpendicular to the geomagnetic field ܤ( ሬԦ ). Therefore the intensity of the polarization electric field is given by

ܧ = ∑ ಹ ∑ ು • ܧ ௬ Eq. ( 18
)
Where

Ground-based magnetic data

The magnetic stations were designed to collect variations of the ,ܪ ܦ and ܼ components of the geomagnetic field during IEEY campaign. Using these data, Doumouya et al. (1998) have estimated the EEJ parameters such as the peak current density, position of the center and the EEJ half-width in a current ribbon assumption. In order to validate the results from ionosonde data by comparison, the EEJ peak current density is estimated from magnetic data using the same method as [START_REF] Doumouya | The equatorial électrojet at African Longitudes: First result from magnetic measurement[END_REF].

The daily regular variations ܵ of the geomagnetic field are estimated in every station by subtracting values of the night level from the measured field according to the following the relationship:

ܵ )ݐ( = )ݐ(ܤ -ܤ Eq. ( 19
)
Where B(t) represents the total measured geomagnetic field at a given local time (t) and B 0 represents the night level. This night level is the threshold from which the daily regular variation ܵ rises. It corresponds to the average of the geomagnetic field during the three hours that spans the two local midnights framing the day of interest.

The equatorial electrojet parameters (position of the center, peak current density and halfwidth) can be estimated from the latitudinal profiles of the EEJ contribution to the daily regular variations of the horizontal and vertical components of the geomagnetic field (Figure 5).

The daily regular variation S r includes the mid-latitude Sq currents effect and the equatorial electrojet contribution respectively symbolized as (ܵ ) and (ܵ ா ) by [START_REF] Fambitakoye | The equatorial electrojet and regular daily variation S R : I. A determination of the equatorial electrojet parameters[END_REF]. In order to isolate the EEJ effects ܵ ா , we remove the ܵ from the total S r .

This approach consists in choosing a threshold from which the EEJ effects start to increase. In that purpose the two stations boarding the meridian chain are considered to be off the EEJ influence area. By interpolating linearly between these stations the ܵ is subtracted from the total S r as follows:

ܵ ா = ܵ -ܵ
Eq. ( 20) [START_REF] Fambitakoye | The equatorial electrojet and regular daily variation S R : I. A determination of the equatorial electrojet parameters[END_REF] have used such an approach with spline interpolation.

Figure 6 presents the diurnal variation of the ܵ ோ )ܪ( and ܵ ா )ܪ( at the EEJ center. It can be noticed that the differences between the amplitudes of ܵ ோ )ܪ( and ܵ ா )ܪ( are relatively weak;

which means that the EEJ magnetic effect is more important at the dip-equator than that of mid-latitude Sq currents around noon.

From the peak amplitude ܪ∆ of the latitudinal profiles of ܵ ா )ܪ( at the EEJ center, we determine the peak current density I 0 using the following Eq. ( 21) [START_REF] Fambitakoye | The equatorial electrojet and regular daily variation S R : I. A determination of the equatorial electrojet parameters[END_REF][START_REF] Doumouya | The equatorial électrojet at African Longitudes: First result from magnetic measurement[END_REF]:

ܫ = ∆ு ( .ସ ௧ ೌ )
Eq. ( 21)

Where h = 105 km is the typical average height of the EEJ, which was established from rocket data (see [START_REF] Fambitakoye | The equatorial electrojet and regular daily variation S R : I. A determination of the equatorial electrojet parameters[END_REF]Doumouya and al., 1998, and references therein), a is the half-width of the EEJ. The half-width is determined according to Eq. ( 22)

after [START_REF] Doumouya | Local time and longitude dependence of the equatorial electrojet magnetic effects[END_REF]:

ܽ = ට ௗ మ ସ -ℎ ଶ Eq. ( 22
)
Where ݀ is the distance between maximum and minimum of latitudinal profiles of the Z component.

Results

Estimating the plasma vertical drift velocity from ionosonde data

The plasma vertical drift velocity is estimated by considering (Eq. 14) which takes into account the time rate of the daily variation of the F layer virtual height (ℎ ᇱ )ܨ and the contributions of the photo chemistry that involves the ionization production and recombination factors. This figure shows that the zonal electric field intensity varies according to the seasons. It is stronger in equinoxes than in solstices (Table 2). On the average, the zonal electric field intensity is comprised between 0.43mV/m and 0.49mV/m during the considered period. The seasonal average values of diverse parameters estimated from the monthly means in the time interval between 10:00 and 14:00LT are shown in Table 2.

Based on Eq. 18, the intensities of polarization electric field ܧ( ) were estimated from the corresponding zonal electric field intensities. Figure 8b shows variations of ܧ from January 1993 to December 1994. The dots correspond to the monthly averages of ܧ and the error bars represent the standard deviations. The polarization field intensity exhibits the same seasonal trend as the zonal electric field. It is also stronger in equinoxes than in solstices.

However the polarization field intensities are found to be about 18 times stronger than that of corresponding zonal electric field. Alken and Maus (2010) found the same results in the American sector. On the average, the polarization electric field intensity is comprised between 7.63mV/m and 9.51mV/m during the considered period. The seasonal averages of the zonal and vertical polarization electric fields around 12:00LT are shown in Table 2 together with the plasma vertical drift velocity.

Estimating the ionospheric current densities from ionosonde data

In the narrow dip-latitude band of ±3° across the dip-equator, when the total vertical current is cancelled around the local noon, only the horizontal eastward Pedersen (Eq. 1) and the Hall currents (Eq. 4) remain [START_REF] Richmond | Ionospheric Electrodynamics[END_REF][START_REF] Onwumechili | The Equatorial Electrojet[END_REF]. Using the monthly values of the zonal and vertical polarization electric fields estimated in the previous section, the eastward Pedersen ܬ( ଵ ) and Hall ܬ( ுଶ ) current densities and the total eastward current density ܬ( ாா ) have been estimated at 105km. Figure 9 presents variations of ܬ ଵ (Figure 9a), ܬ ுଶ (Figure 9b) and ܬ ாா (Figure 9c) from January 1993 to December 1994. The dots correspond to the monthly averages of the current densities and the error bars represent the standard deviations. The three current densities exhibit the same trend of seasonal variations.

However it is to be noticed that the amplitude of the eastward Pedersen current density is about 300 times weaker than the eastward Hall current density. During the two years the amplitude of ܬ ଵ varies approximately between 12.10 -3 A/km 2 and 16.10 -3 A/km 2 , while ܬ ுଶ is comprised between 3.63 A/km 2 and 5.80 A/km 2 . The yearly mean values of the eastward Pedersen current density are respectively (15.1 ± 2.3).10 -3 A/km 2 in 1993 and (13.3 ± 1.9).10 -3

A/km 2 in 1994, and that of the Hall current density are (4.98 ± 0.98) A/km 2 in 1993 and (4.45 ± 0.75) A/km 2 in 1994. As consequence, the eastward Pedersen current density appears to be negligible with respect to the eastward Hall current density. Thus the equatorial electrojet current density ܬ( ாா ) in Figure 9c appears to be in the same order as the eastward Hall current density.

Estimating the EEJ peak current density from ionosonde data

Assuming the equatorial electrojet as a thin current ribbon that circulates at 105km altitude, the integrated peak current density (I 0 ) at its center can be considered as a proxy of the EEJ strength [START_REF] Fambitakoye | The equatorial electrojet and regular daily variation S R : I. A determination of the equatorial electrojet parameters[END_REF], Doumouya et al., 1998). In order to evaluate the electric fields and current densities determined in the previous sections, an estimate of the integrated peak current density (I 0 ) is made in this section. Thus EEJ current density ܬ ாா was integrated over the thickness of the E-layer. In this purpose a uniform height distribution of ܬ ாா was assumed. Thus I 0 was obtained by multiplying ܬ ாா times the mean thickness (݁ ா ) of the Elayer (Eq. 23).

ܫ = ܬ ாா . ݁ ா Eq. ( 23)

The E layer thickness (݁ ா ) is approximately estimated between 90km and 140km altitudes, that is

݁ ா = 50 ݇݉.
The EEJ peak current density (I 0 ) at the center is usually estimated from EEJ magnetic variations observed at the dip-equator [START_REF] Fambitakoye | The equatorial electrojet and regular daily variation S R : I. A determination of the equatorial electrojet parameters[END_REF], Doumouya et al., 1998). In order to validate ionosonde inferred electrodynamics parameters, the EEJ peak current density (I 0 ) was estimated from ground-based magnetic data recorded during the same time period according to (Eq. 21). In the next section the EEJ integrated peak current densities ( ) obtained from ionosonde data are compared with that inferred from magnetic data.

Comparison between parameters inferred from magnetometer and ionosonde data.

In this section correlation between the EEJ magnetic effect and the vertical ܧ ሬԦ × ܤ ሬԦ drift velocity is examined, and the EEJ integrated peak current densities estimated from ionosonde magnetic data are compared. Figure 10 shows a fairly good linear correlation between the peak amplitude of the EEJ magnetic effect ( ܪ∆ ) at the EEJ center and the vertical drift velocity ܸ ௗ , with a correlation coefficient R= 0.74.

Figure 11 compares the seasonal averages of the EEJ integrated peak current density estimated from ionosonde data (red circles) and magnetic data (black dots). The seasonal averages of the integrated peak current density (I 0 ) obtained from ionosonde data ( ) are given in Table 2. According to Figure 11 the values of are higher than that of in most cases. The highest difference between and is 62.97A/km. This value is larger than the standard deviations of 45A/km obtained in previous studies by [START_REF] Doumouya | The equatorial électrojet at African Longitudes: First result from magnetic measurement[END_REF].

However, the results from both experiments are relatively close. The root-mean-square (rms) deviation between and is 15.91A/km. Furthermore and remarkably exhibit similar trend for the seasonal variability, with maxima during the equinoxes and minima during the solstices. In addition, the effects of the decreasing phase of the solar cycle between 1993 and 1994 can be noticed as well.

Discussion and conclusion

In the present work, some characteristic parameters of the equatorial electrojet have been estimated on the basis of the IPS-42 ionosonde data at Korhogo. The results have been compared with that obtained from magnetic data. This study consisted of determining the zonal electric field through an estimate of the plasma vertical ܧ × ܤ drift velocity from ionosonde data. In that purpose, the apparent plasma vertical drift velocity (ܸ') that corresponds to the time rate of the diurnal variations of the F-layer virtual height, and the photo chemical effects that include the ionization production and recombination were considered. Note that in most studies, the F-layer vertical drift velocity was estimated by the time rate of the F-layer virtual height during periods of dominant electric convection like the pre-reversal enhancement [START_REF] Abdu | Magnetic declination control of the equatorial F regin dynamo electric field development and spread F[END_REF][START_REF] Abdu | Equatorial F layer heights, evening prereversal electric field, and night E-layer density in the American sector. IRI validation with observations[END_REF][START_REF] Abdu | Equatorial F region evening vertical drift, and peak height, during southern winter months: A comparison of observational data with the IRI descriptions[END_REF][START_REF] Batista | Equatorial F-region vertical plasma drifts: Seasonal and longitudinal asymmetries in the American sector[END_REF]Subbarao and Krishna Murthy, 1993;[START_REF] Hari | Equatorial night-time f-region zonal electric fields[END_REF]Batista et al., 1996;[START_REF] Bittencourt | A theoretical comparison between apparent and real vertical ionization drift velocities in the equatorial F-region[END_REF][START_REF] Oyekola | Morphology of F-region vertical ܧ × ܤ drifts in the African sector using ionosonde measurements[END_REF][START_REF] Adebesin | Equatorial vertical plasma drift velocities and electron densities inferred from ground ionosonde measurements during low solar activity[END_REF]. For the present study, we estimated the photo chemical effects according to the approach used by Iheonu and Oyekola (2005) and [START_REF] Oyekola | Morphology of F-region vertical ܧ × ܤ drifts in the African sector using ionosonde measurements[END_REF]. It is to be noticed that this approach significantly improved the estimated daytime F-layer plasma vertical drift velocity.

The trend of the daily variation of the plasma vertical drift velocity is roughly same as that obtained from previous studies by Bonelli and Carvalho, 1993;Batista et al., 1996;[START_REF] Scherliess | Radar and satellite global equatorial F-region vertical drift model[END_REF]; G. [START_REF] Ning | The correlation of longitudinal/seasonal variations of evening equatorial pre-reversal drift and of plasma bubbles[END_REF]. Indeed, the main features such as the prereversal enhancement around 19:00 are also observed in Figure 7. The day-time dome with a maximum around 12:00 is observed in all seasons as that obtained by Scherliess andFejer (1999) and[START_REF] Ning | The correlation of longitudinal/seasonal variations of evening equatorial pre-reversal drift and of plasma bubbles[END_REF]. The noontime averages of the drift velocity shown in Table 2 vary according to seasons. They are higher in equinoxes than in solstices. values of the daytime vertical drift velocity also range between about 10m/s to 30m/s. Our results range well in the intervals of [START_REF] Anderson | Global, low-latitude, vertical ExB drift velocities inferred from day-time magnetometer observations[END_REF][START_REF] Ning | The correlation of longitudinal/seasonal variations of evening equatorial pre-reversal drift and of plasma bubbles[END_REF]. However, possible differences between our result and that obtained by [START_REF] Anderson | Global, low-latitude, vertical ExB drift velocities inferred from day-time magnetometer observations[END_REF] altitudes, the integrated peak current density ܫ( ) at the EEJ center has been estimated as well.

In order to evaluate the method of estimating these parameters, the IPS-42 ionosonde based integrated peak current density ܫ( ) has been compared with that obtained from ground-based magnetic observations ܫ( ). The values obtained from the two methods are found to be in the same order. In addition, their seasonal variations and dependence on the solar activity are found to be similar.

This study has shown that more basic parameters of the equatorial electrojet can be accessible with a good accuracy, if the daytime F-region plasma vertical drift velocity can be accurately estimated. Unfortunately, in contrast of the American sector with the Jicamarca VHF radar, the lack of VHF radar continuous measurements near the dip equator in the African longitude sectors, does not allow such study. The HF radar used at Korhogo during the IEEY [START_REF] Blanc | Typical disturbances of the daytime equatorial F region observed with a high-resolution HF radar[END_REF] operated only from March to July, 1993.

List of tables

Table 1: Geographic coordinates of the magnetic stations installed along the meridian 5°W in West Africa during the International Equatorial Electrojet Year.

Figure 3

 3 shows the average daily variations of ℎ ᇱ ܨ for different seasons in 1993 (Figure3a, the left column) and 1994 (Figure3b, the right column). From top to bottom, each panel corresponds to a particular season. March equinox (top row) includes February, March and April; June solstice (2 nd row) includes Mai, June and July; September equinox (3 rd row) includes August, September and October, and finally December solstice (bottom row) includes November, December and January. The dots represent the ℎ ᇱ ܨ seasonal averages for each 15 minute time interval and the solid curves represent the mean daily variations in different seasons. After a decrease toward a minimum around 5:00LT for June and December solstices, the height ℎ ᇱ ܨ increases from 6:00LT to attain a maximum around 12:00LT; it decreases slowly between 12:00 and 15:00 LT. It briskly increases around 18:00LT before a sharp decrease between 19:00LT and 21:00LT.

  ∑ and ∑ ு are respectively the integrated Pedersen and Hall conductivities along the field lines. The values of ∑ and ∑ ு are estimated through the local conductivities obtained from the International Reference Ionosphere (IRI-2012) model (Bilitza and al, 2012) from the website (http://wdc.kugi.kyoto-u.ac.jp). Figure 4 schematically summarizes the ionosonde data processing method. The first step of this approach consists of estimating the zonal electric field from the ionosonde inferred vertical drift velocity, and the polarization electric field by using integrated Pedersen (∑ ) and Hall (∑ ு ) conductivities. In a second step, various current densities such as Pedersen, Hall and the net eastward EEJ current densities are estimated. Details of various calculations are based on the equations that have been developed in section 2. The integrated peak current density ܫ( ) at the EEJ center is estimated by height integrating the net eastward EEJ current density.

Figure 7

 7 Figure 7 displays the daily variation of the mean vertical drift velocity in different

  For all the seasons the noontime average values of the vertical drift velocity at Korhogo range 13.56m/s and 15.61m/s Anderson et al. (2006) estimated the vertical drift velocity in 3 longitude sectors from January 2001 to December 2004. They found a minimum value of 10 m/s in equinox and maximum values that attain 25m/s. According to Figure 1 of Li et al (2007), based on satellite ROCSAT-1 observations in 5 longitude sectors and different seasons in period 2000-2002, the

  [START_REF] Ning | The correlation of longitudinal/seasonal variations of evening equatorial pre-reversal drift and of plasma bubbles[END_REF] can be explained by the dependence of the vertical drift velocity on the longitudes, and also on the solar cycle. Indeed the period 1993-1994 was in the decreasing phase close to the end minimum of the solar cycle 22. In contrast, the studies of[START_REF] Anderson | Global, low-latitude, vertical ExB drift velocities inferred from day-time magnetometer observations[END_REF] and Li et al (2007) concerned the period which included the maximum of solar cycle 23. The seasonal average values of the zonal electric field range 0.47mV/m and 0.46mV/m during the period 1993-1994, in West Africa. The estimated zonal electric field, the IRI-2012 model ionospheric conductivities, and the IGRF-10 model geomagnetic field intensity have been used to estimate the vertical polarization electric field ܧ( ሬሬሬሬԦ ), the eastward Pedersen ܬ( ଵ ሬሬሬሬሬԦ ) and Hall ܬ( ுଶ ሬሬሬሬሬԦ ) current densities, and the net eastward EEJ current density ܬ( ாா ሬሬሬሬሬሬሬԦ ). By height integrating the net eastward EEJ current density between 90km and 140km

Figure captions Figure 1 :

 captions1 Figure captions

Figure 2 :

 2 Figure 2: The 5°W meridian chain magnetic stations (asterisk) and the ionosonde (triangle)

Figure 3 :

 3 Figure 3: Daily trend of the F layer virtual heights ℎ'ܨ from the ISP-42 ionosonde data in 1993 (a) and 1994 (b). The dots indicate the seasonal average of the F layer virtual height at

Figure 4 :

 4 Figure 4: diagrams of the method used to process ionosonde data for the estimation of the

Figure 5 :

 5 Figure 5: Latitudinal profiles of the regular daily variation Sr of the D, H and Z components

Figure 6 :Figure 7 :

 67 Figure 6: Daily regular variation of the horizontal component (H) of the geomagnetic field. The dashed red lines represent the total daily regular variation ܵ ,)ܪ( and the solid blue lines represent the equatorial electrojet contribution ܵ ா )ܪ( in the daily regular variation ܵ .)ܪ(

Figure 8 :

 8 Figure 8: Seasonal variations of the Zonal electric field ܧ ௬ (a) and Polarization electric field ܧ (b). The dots represent the monthly averages of ܧ ௬ respectively ܧ from January 1993 to December 1994, the error bars indicate the standard deviations.

Figure 9 :

 9 Figure 9: Variation of the eastward Pedersen (a), Hall (b) and total electrojet (c) current

Figure 10 :Figure 11 :

 1011 Figure 10: Correlation between the EEJ magnetic effect ܪ∆ and the vertical drift velocity ܸ ௗ

Figure 1 :

 1 Figure 1: Mechanism of the equatorial electrojet current flow in the E-region is described in three steps. Step 1: zonal electric Ey (red arrow), magnetic field B (green cross-circle), downward Hall current density (dashed wide arrow) and the eastward Pedersen current (solid wide arrow). Step 2: vertical polarization electric Ep (blue arrow), magnetic field B (green cross-circle), upward Pedersen current density (dashed wide blue arrow) and the eastward Hall current density (solid wide blue arrow). Step 3: The total EEJ current density (wide pink arrow).

Figure 2 :

 2 Figure 2: The 5°W meridian chain magnetic stations (asterisk) and the ionosonde (triangle)

Figure 3 :

 3 Figure 3: Daily trend of the F layer virtual heights ℎ'ܨ from the ISP-42 ionosonde data in 1993 (a) and 1994 (b). The dots indicate the seasonal average of the F layer virtual height at

Figure 4 :

 4 Figure 4: Diagrams of the method used to process ionosonde data for the estimation of the

Figure 5 :

 5 Figure 5: Latitudinal profiles of the daily regular variation Sr of the H and Z components of the geomagnetic field, on 24 February 1993.

Figure 6 :Figure 7 :

 67 Figure 6: Daily regular variation of the horizontal component (H) of the geomagnetic field. The dashed red lines represent the total daily regular variation ܵ ,)ܪ( and the solid blue lines represent the equatorial electrojet contribution ܵ ா )ܪ( in the daily regular variation ܵ .)ܪ(

Figure 8 :

 8 Figure 8: Seasonal variations of the Zonal electric field ܧ ௬ (a) and Polarization electric field ܧ (b). The dots represent the monthly averages of ܧ ௬ respectively ܧ from January 1993 to December 1994, the error bars indicate the standard deviations.

Figure 9 :

 9 Figure 9: Variation of the eastward Pedersen (a), Hall (b) and total electrojet (c) current

Figure 11 :

 11 Figure 11: Comparison of the peak current density (I 0 ) of the equatorial electrojet obtained

Table 2 :

 2 Seasonal averages of the plasma vertical drift velocity (ܸ

ௗ ), the zonal )ݕܧ( and polarization )ܧ( electric fields, the eastward Pedersen ܬ( ) and Hall ܬ( ு ) current densities, and the net eastward current density ܬ( ாா ) between 10:00LT and 14:00LT in 1993 and 1994.

Table 1 : Geographic coordinates of the magnetic stations installed along the meridian 5°W in West Africa during the International Equatorial Electrojet Year.

 1

	Stations	Code	Geographic	Dip Lat.(°)
			Lat(°N)	Long(°W)
	Tombouctou	Tom	16.733	3.000	6.76
	Mopti	Mop	14.508	4.087	4.02
	San	San	13.237	4.879	2.45
	Koutiala	Kou	12.356	5.448	1.38
	Sikasso	Sik	11.344	5.706	0.12
	Nielle	Nie	10.203	5.636	-1.30
	Korhogo	Kor	9.336	5.427	-1.88
	Katiola	Kat	8.183	5.044	-3.85
	Tiebissou	Tie	7.218	5.241	-5.04
	Lamto	Lam	6.233	5.017	-6. 30

Table 2 :

 2 Seasonal averages of the plasma vertical drift velocity (ܸ ௗ ), the zonal )ݕܧ( and polarization )ܧ( electric fields, the eastward Pedersen ܬ( ) and Hall ܬ( ு ) current densities, the net eastward current density ܬ( ாா ) and the peak current density ܫ( ) at the center of the equatorial electrojet around noontime in 1993 and 1994.Ioi (A/km)290.80 252.03 260.55 196.12 253.93 218.43 238.68 182.14

			1993			1994
		M. Eq J. Sol S. Eq D. Sol	M. Eq	J. Sol	S. Eq D. Sol
	V d (m/s)	15.61	15.01 15.30	13.81	15.03	14.01	15.01 13.56
	Ey (mV/m)	0.49	0.47	0.48	0.44	0.48	0.47	0.48	0.43
	Ep (mV/m)	9.51	8.41	8.98	7.61	9.22	7.93	8.81	7.63
	J P1 (10 -3 A/km 2 )	15.8	16.3	15.3	13.0	13.6	13.6	14.0	11.7
	J H2 (A/km 2 )	5.80	5.02	5.19	3.90	5.06	4.35	4.75	3.63
	J EEJ (A/km 2 )	5.82	5.04	5.21	3.92	5.07	4.36	4.76	3.64

Acknowledgement

The IPS-42 ionosonde was operated by the Centre National d'Etude de Télécommunication (CNET) France and the network of 10 magnetic stations by ORSTOM (now IRD) during the International Equatorial Electrojet Year (IEEY). The student Franck Oswald Grodji has received a grant from the Government of Cote d'Ivoire for his PhD study.


Bruno Cessac

Pierre Kornprobst

S Kraria

H Nasser

Daniela Pamplona

Geoffrey Portelli

Thierry Viéville

ENAS: A new software for spike train analysis and simulation

ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

ENAS provides statistical analysis with Maximum Entropy-Gibbs distributions taking into account both spatial and temporal correlations as constraints, allowing to introduce causality and memory in statistics.

Virtual Retina simulator

Other features: Crop and bin rasters, select neurons subsets according to different criteria, set MEA array configuration, generate rasters from given statistics As one gains more intuitions and results on the importance of concerted activity in spike trains, models are developed to extract potential canonical principles underlying spike coding. These methods shed a new light on spike train dynamics. However, they require time and expertise to be implemented efficiently, making them hard to use on a daily basis by neuroscientists or modelers. To bridge this gap, we developed the license free multiplatform software ENAS integrating tools for spike trains analysis and simulation.

ENAS includes a virtual retina simulator that includes feedback connections from the bipolar to the OPL layer and lateral connections in the IPL. This simulator maps images into spikes in a bio plausible way.

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  https://enas.inria.fr Free B. Cessac 1 -P. Kornprobst 1 -S. Kraria 1 -H. Nasser 1 -D. Pamplona 1 -G. Portelli 1 -T. Viéville 2 1: Université Côte d'Azur, Inria, Biovision team, France 2.cessac@inria.fr This work was supported by the French ministry of Research and University of Nice (EDSTIC), INRIA ADT, ERC-NERVI number 227747, KEOPS ANR-CONICYT, the European Union Project Renvision #600847 and by the ECOS-Sud program (grant C13E06).