Charlotte Héricé

Radwa Khalil

Marie E Moftah

Thomas Boraud

Martin Guthrie

André É Garenne
email: andre.garenne@u-bordeaux.fr

Charlotte H Éric É

Decision making under uncertainty in a

Keywords: Basal ganglia, decision making, connectionist models, action selection

Introduction

Decision making is a process that permits an organism to choose an action [START_REF] Lee | Neural basis of reinforcement learning and decision making[END_REF] from among several alternatives. This process is performed by a complex network consisting of cortical and sub-cortical structures, among which the basal ganglia (BG) and thalamus play a major role. Over the past two decades, the BG have gradually been regarded as involved in selecting motor actions [Mink, 1996, Kropotov and Etlinger, 1999, Redgrave et al., 1999] and are now also known to have limbic and cognitive roles [START_REF] Bar-Gad | Information processing, dimensionality reduction and reinforcement learning in the basal ganglia[END_REF]. The structures of the BG therefore have an important role in information processing at the heart of the nervous system. However, even though their patterns of connectivity have been in large part described [START_REF] Gurney | A computational model of action selection in the basal ganglia. i. a new functional anatomy[END_REF] their complexity is such that they are difficult to analyze formally.

Many models and functional hypotheses have been developed since the original box and arrow description of connectivity was developed more than 25 years ago [START_REF] Albin | The functional anatomy of basal ganglia disorders[END_REF], Alexander et al., 1986]. These have attempted to understand the dynamic interactions between the different pathways and their consequences for functionality [START_REF] Bar-Gad | Stepping out of the box: information processing in the neural networks of the basal ganglia[END_REF], Mink, 1996, Redgrave et al., 1999, Suri and Schultz, 1999]. For instance in the computational study of Suri [START_REF] Suri | A neural network model with dopamine-like reinforcement signal that learns a spatial delayed response task[END_REF], a single compartment represents a neuronal subpopulation that describes a given region. The transfer of information between the compartments is represented by scalar numeric activity values. This formalism provides mesoscopic views of information exchange and show dynamic characteristics that are compatible with behavioral and electrophysiological experimental results [START_REF] Berthet | Action selection performance of a reconfigurable basal ganglia inspired model with hebbian-bayesian go-nogo connectivity[END_REF], Frank et al., 2001, Leblois et al., 2006a, Sukumar et al., 2012]. It has the major advantage of being computationally tractable because, in general, a single differential equation allows an entire area to be simulated. Moreover, the parameter space is relatively small generally because the parameters are mainly used to control interactions between compartments. On the other hand, it is infrequent that an attempt is made to describe behavioral findings by means of an integrated neural model. Here we define the integrated neural model as a bottom-up designed architecture in which elementary building blocks represent spiking neurons and synaptic subunits and of which assembly covers a whole neuronal system. For a deeper understanding of complex central nervous system mechanisms, it is necessary at some point to attempt a description at this level. For example, this can be useful to demonstrate the relation between a pathophysiological or pharmacological mechanism described at the cellular scale and its impact on the properties of whole nervous system regions. It is therefore clear that these steps need to be taken in parallel with the development of models at a coarser scale. The idea of an integrated neural model should thus be seen as a supplementary guarantee of validity and an improvement in the predictive capacities of mesoscopic computational models (e.g., population rate-models). Along with the difficulties inherent in neuronal scale models, are the need for a great deal of computational power, the combinatorial explosion of their dimensionality and the resulting difficulty in adjusting the system parameters. Despite these difficulties, some studies of neuronal networks of small and medium size have shown both their feasibility and the pertinence of their results [START_REF] Sarvestani | A computational model of visually guided locomotion in lamprey[END_REF]. Moreover, large scale projects already exist that apply this approach with a view to the integration and multi-scale coherence of the computational model produced [START_REF] Hines | Fully implicit parallel simulation of single neurons[END_REF], Migliore et al., 2006].

In this study we have developed a neural network model mainly inspired by previous architecture and dynamical properties initiated by Leblois [Leblois et al., 2006a] and extended by Guthrie [START_REF] Guthrie | Interaction between cognitive and motor cortico-basal ganglia loops during decision making: A computational study[END_REF]. The initial tasks chosen to test the characteristics of the computational model for this study come from behavioral and electrophysiological recordings made in non-human primates by our team [START_REF] Piron | The globus pallidus pars interna in goal-oriented and routine behaviors: Resolving a long-standing paradox[END_REF], Pasquereau et al., 2007]. The neural architecture has been modified [Mink, 1996, Nambu, 2011] to include additional circuitry details. The first difference in our approach is that, instead of using population rate-models, we have implemented spiking neurons and synaptic units circuits with a higher level of detail and dynamics. Moreover we have submitted the resulting model to additional tests and protocols. We have first reproduced previous modeling results regarding the role of BG loops in optimal decision making learning with this new model. We have then shown that it was able to perform classes of tasks that have not previously been demonstrated in this type of model. First the model was able to switch to a different learning task with good performances and without requiring intrinsic modification. Second it was able to perform additional behavioral processes related to such as reversal learning and extinction protocol. Third the model was also able to reproduce the effect of partial lesion studies in a consistent manner. Our spiking neuron-based description of the BG system has thus shown, in addition to several innovative results, its coherence with previous population rate models and moreover, it offers the possibility of investigating the effect of cell-level mechanisms on the global BG network properties.

Behavioral task

Electrophysiological and behavioral data have been obtained from macaque monkeys in two center-out reinforcement learning tasks [START_REF] Pasquereau | Shaping of motor responses by incentive values through the basal ganglia[END_REF], Piron et al., 2016]. In the first task, a typical session consisted of series of trials in which four different target shapes (four-cue protocol) were used, each associated with a different reward probability (P(R)) of 0, 0.33, 0.66 and 1).

On each trial, two of the cues were selected pseudo-randomly such that each of the six possible cue combinations was presented 20 times in a complete session.

Our simulation sessions thus contained 120 trials. In the second task only two different cues were used with P(R)s of 0.25 and 0.75. In both cases, the aim for the monkeys was to select the cue with the highest reward probability in order to maximize the reward delivered (fruit juice). Extra-cellular recordings were performed simultaneously in the left Globus Pallidus pars interna (GPi) and in the dorsal striatum.

Analysis of the electrophysiology suggests that the cues used in the first behavioral task [START_REF] Pasquereau | Shaping of motor responses by incentive values through the basal ganglia[END_REF] can be decomposed into a cognitive aspect (the cue shape) and a motor aspect (the direction to move). We have therefore modeled this as two sets of action selection loops in parallel. Each action selection loop is represented as an area of cortex in closed-loop feedback through the BG with itself. These loops also comprise associative areas of cortex and striatum that represent a compression of the two dimensions of the cue. Associative cortex inputs to the striatum are assumed to be a high-level visual representation (arising from parietal cortical areas) that is a combination of both the cue shape and position [START_REF] Guthrie | Interaction between cognitive and motor cortico-basal ganglia loops during decision making: A computational study[END_REF]. The four possible cue shapes are associated with four cognitive cortical subpopulations and a similar distribution is applied to direction/motor subpopulations. There are therefore 16 possible combinations of cue shape and direction, each represented by a subpopulation in associative cortex and striatum. For instance if two cues are shown in two positions on each trial, only two of the cognitive, two of the motor and two of the corresponding cortical associative subpopulations will be activated on each trial. For clarity and ease, we will use the following nomenclature in this paper. The target shapes will be named C0, C1, C2 and C3 (where C means cortical "cognitive" subpopulations) and the motor directions will be named M0, M1, M2 and M3. The P(R) will be distributed as follow: C0: 0, C1: 0.33, C2: 0.66 and C3: 1. The second task has two different cues with P(R) of 0.25 and 0.75 that are represented in the same four locations and processed in a similar manner (two-cue protocol).

Model architecture

A general schema of the circuitry involving the cortex, BG and thalamus is shown in Figure 1. There are three main pathways that form cortico-cortical loops through the BG. The direct pathway (i) overall exerts an excitatory (positive) feedback that is convergent and focused [START_REF] Percheron | A golgi analysis of the primate globus pallidus. iii. spatial organization of the striato-pallidal complex[END_REF]. In contrast, the hyperdirect pathway (ii) exercises an inhibitory feedback that is widespread due to divergence of connections from the subthalamic nucleus (STN) to the GPi. The interaction between these two pathways has a tendency to amplify any difference between cortical networks activating different direct pathway loops [Mink, 1996]. The indirect pathway (iii) has not been included in this modeling study for various reasons. It was originally thought to provide a closed, negative feedback loop [START_REF] Albin | The functional anatomy of basal ganglia disorders[END_REF], but with further delineation of anatomical connections, would seem to form a sub-network with internal positive and negative feedback loops, at the heart of the BG [START_REF] Bevan | Synaptic targets of physiologically, neurochemically and morphologically characterized neurons of the rate globus pallidus[END_REF], Kita and Kita, 1994, Smith and Bolam, 1989]. With this proliferation of anatomical complexity, it is no longer clear that the indirect pathway forms a closed cortico-subcortical loop that would be able to transfer precise spatiotemporal information [Levy, 1997]. Divergence both in the Globus Pallidus pars externa (GPe)-STN and the GPe-striatum sub-loops [START_REF] Bevan | Synaptic targets of physiologically, neurochemically and morphologically characterized neurons of the rate globus pallidus[END_REF], Chang et al., 1981, Gerfen, 1985] as well as local GPe axon collaterals [START_REF] Bevan | Synaptic targets of physiologically, neurochemically and morphologically characterized neurons of the rate globus pallidus[END_REF], Brown et al., 1998] would suggest that this is unlikely.

We have also taken into account the effect of medium spiny neurons lateral inhibition (LI) in striatal populations of our model. The exact functional role of these connections remains mostly unknown or controversial but in a neuronal population LI often plays a role in information processing [Schaette andKempter, 2012, Ghodratitoostani et al., 2016]. Recent studies has emphasized LI involvement in the striatum where it tends to increase the signal-to-noise ratio [START_REF] Moyer | Lateral and feedforward inhibition suppress asynchronous activity in a large, biophysically-detailed computational model of the striatal network[END_REF] and also the BG capability to deal with complex tasks [START_REF] Berthet | Functional relevance of different basal ganglia pathways investigated in a spiking model with reward dependent plasticity[END_REF].

The network inputs are sensory representations of the environmental cues and the action selection occurs over the course of many circuits through the loops. [START_REF] Bar-Gad | Information processing, dimensionality reduction and reinforcement learning in the basal ganglia[END_REF], Moyer et al., 2014].

,

The model architecture is initially based on that of Leblois [Leblois et al., 2006a] and Guthrie [START_REF] Guthrie | Interaction between cognitive and motor cortico-basal ganglia loops during decision making: A computational study[END_REF] and has been adapted to represent the task under consideration and additional circuitry (cf. Figure 2). The small number of neurons in each subpopulation is a tradeoff which approximately takes into account relative structure sizes [START_REF] Schroll | Dysfunctional and compensatory synaptic plasticity in parkinson's disease[END_REF]. It was chosen for computational tractability and not to represent exact neuronal population ratios [START_REF] Humphries | A physiologically plausible model of action selection and oscillatory activity in the basal ganglia[END_REF]. The subpopulation sizes are: cortex, 100; striatum, 40; STN, 10; GPi 10; thalamus, 20. The total network size is 3,680 neurons and the connectivity ensemble between regions comprises 723,200 synapses. This provides a network of sufficient size to produce realistically complex synaptic interactions, but still computationally tractable on a standard desktop computer.

Analysis of cortical activity

As well as representing the salience of the sensory inputs, cognitive and motor cortical activity also serve as detectors of the choice made and therefore the behavior of the animal. Presentation of the cues is simulated by an additional current injection into the corresponding cortical subpopulations [cf. Figs. 3(b) and 3(c)]. Each simulated trial lasts 1 second from the presentation of the stimuli. Each ms, the spikes timestamps of each neuron are recorded in parallel with behavioral events, reward scores and cognitive cortico-striatal synaptic weight values. For each neuronal subpopulation i of size N neurons (i), an average firing rate (i) is computed each ms and expressed in Hz:

α(i) = N spikes (i) N neurons (i) .10 3 , (1)
where N spikes (i) is the number of recorded spikes during this ms. To link the spiking activity of the model to the behavior and thus to define when the decision to choose a particular target is made, we compute the difference in average firing rates between the two activated subpopulations. When this difference surpasses a threshold value of 40 Hz [START_REF] Guthrie | Interaction between cognitive and motor cortico-basal ganglia loops during decision making: A computational study[END_REF] this is referred to as symmetry breaking and the movement selection is then designated by the cortical motor subpopulation that has the highest firing rate. During a trial this symmetry breaking can be seen in both the cognitive and motor loops. In the motor cortex, it is interpreted as the onset of a movement in one direction (M0, M1, M2 or M3). A reward is then given or withheld based on the P(R) of the target chosen by the movement. If the movement is toward the target shape with the highest P(R), this is considered as a good choice (GC) even if no reward is given. Similarly a good decision (GD) occurs when the activity of the cognitive cortical subpopulation associated with the highest P(R)

is greater than the activity of the cognitive cortical subpopulation associated with the other presented cue.

Model implementation

This study required a neuronal model that was sufficiently simple to be implemented in a large-scale network. To restrict the complexity and the size of the parameter space of the model, we have chosen a leaky integrate-and-fire neuron (LIF):

C. dV m (t) dt + V m (t) -V rest R = I(t) + ξ(t), (2)
if V m (t) > V thres : V m (t) ← V rest , (3)
where V m (t) is the membrane potential and V rest the resting potential.

Default values are: C=10 -10 F, R = 10 8 ohms, V rest =-65 mV, V thres =-55 mV and refractory period is 1 ms. ξ(t) is a gaussian white noise current which simulates synaptic bombardment [START_REF] Neymotin | Emergence of physiological oscillation frequencies in a computer model of neocortex[END_REF] and I(t) the externally applied current. The network was built using voltage-jump weighted synapses.

The interneuronal transmission delays based on [START_REF] Humphries | A physiologically plausible model of action selection and oscillatory activity in the basal ganglia[END_REF] and weights necessary for coherent model dynamics are summarized in Table 1. To simulate the network physiological basal activity, a base current was applied in the network in addition to the synaptic noise ξ(t).

The model was developed with GNU C++ 4.9 library and numerical equations were solved using a first order forward Euler algorithm with a one ms time step. Simulation were run using Monte Carlo methods. Data analysis and visualization were performed with python-matplotlib [Hunter, 2007] and R [R-Team, 2015].

Table 1: Synaptic weights and delays used in the connections between subpopulations of the circuit (M: motor, C: cognitive, A: associative).

Connexion

Weight (mVolt) Delay (ms)

Cortex (M/C) → Striatum (M/C) 0.1 11 Cortex (M/C) → Striatum (A) 0.035 11 Cortex (A) → Striatum (A) 0.02 11 Cortex (M/C) → STN 0.125 6 Cortex (M/C) → Thalamus 0.125 5 STN → GPi 2 2 Thalamus → Cortex 10 5 Striatum → GPi -5 6 Striatum → Striatum -0.25 2 GPi → Thalamus -10 5

Plasticity and learning

As this first study is essentially looking to show how the decision making capabilities and learning take place, we have chosen to implement a simple LTP/LTD weight update rule driven by the presence or absence of a reward following a move in an outcome specific manner [START_REF] Cools | Striatal dopamine predicts outcome-specific reversal learning and its sensitivity to dopaminergic drug administration[END_REF]]. In the model, learning occurs only at the cognitive cortico-striatal synapse where phasic changes in dopamine concentration have been shown to be necessary for the production of long-term synaptic weight variations [START_REF] Pawlak | Dopamine receptor activation is required for corticostriatal spike-timing dependent plasticity[END_REF], Kerr and Wickens, 2001, Reynolds et al., 2001]. When a chosen target results in a reward, all the weights of the cognitive cortico-striatal projections contributing to the choice of this target are slightly increased. In all other outcome situations, they are decreased. The synaptic weight variation rule is computed as follow:

w i,j (n + 1) = w i,j (n) + η.∆G, η = w max -w i,j (n) w max -w min , (4)
where w i,j is the weight of the synapse between cells i and j, η the learning rate and ∆G an increment that was set to 5% of the average weight values.

η depends on the current w i,j value and the resulting weight variation curve follows a Sutton-Barto model [Klopf, 1988].

Results

Parameterization and model behavior

The first stage of the setup of the model was to simultaneously adjust the various parameters to produce average firing rate activities in the different regions that were in accordance with those observed in vivo. For example, striatal activity is generally very low compared to cortical activity or GPi activity [START_REF] Pasquereau | Shaping of motor responses by incentive values through the basal ganglia[END_REF]. In the same way, thalamic activity shows large variation in the model, but the range of frequencies observed remains in accordance with experimental data [START_REF] Chen | Neuronal firing in the ventrolateral thalamus of patients with parkinson's disease differs from that with essential tremor[END_REF].

As previously mentioned, we apply a Monte Carlo approach to run our simulations. Due to randomization in the assignment of initial weights and conduction delays, each network model is unique. To rule out the possibility of a sample effect on the functional properties of the networks, 30 simulations were run for each of the six possible cue combinations. consistent with the input pattern and no significant difference was found in each of the 72 subregions between the 30 generated networks. Therefore, there is no noticeable "network effect" on the model dynamics and all of the generated models behave in a comparable way.

As shown in Fig. 3(a), the stimulated cortical regions have a higher average frequency, as would be expected. Referring to Fig. 2 for the connectivity, propagation of information through the network can also be observed. The striatal cognitive and motor subpopulations are activated in a similar pattern to the corresponding cortical areas. Subpopulations in the associative striatal region receive the sum of cognitive, motor and associative cortical inputs. In Figure 3(a), peaks in A10 and A13 and, to a lesser extent (due to the lack of additional associative cortex input) in A9 and A14 can be observed in striatal subpopulations. Activity in the STN is aligned with that of cortex. In the GPi the activities observed are the inverse of those seen in the cognitive and motor subpopulations of striatum. This is consistent with the known action of the inhibitory outputs from striatum. Finally, thalamic activity is balanced by excitation from cortex and inhibition from GPi and differences in activity are therefore amplified. This amplification is the mechanism that leads to symmetry breaking, where the activity in one channel increases while that in the other channel decreases.

Dynamic action selection

In the absence of learning the network is still able to make a decision. At the start of a trial, the presentation of the two targets leads to the activation of two channels in the positive feedback direct pathway loop. Symmetry breaking between the two channels occurs as follows: because the loop gain of the direct pathway is greater than one, differential activation of one channel due to noise is amplified. The resultant increased cortical activation starts a positive feedback takeoff in that channel specifically because direct pathway channels are segregated. The increase of average firing rates measured in this channel finally reaches a plateau that leads to a stabilization of all the subregions activities in the system [cf. Fig. 4(a)]. This upper bound results from the model constraints, notably regarding the circuitry, the conduction delays and the cellular properties. But the increased cortical activation of one channel also increases the input to the divergent, negative feedback hyperdirect pathway causing suppression of all channels, especially the competing channel. A small difference in channel activations due to noise thus leads to one channel being highly activated to the detriment of the others.

In a naïve network, the symmetry breaking should select one of the two subpopulations with equal probabilities and the average GC rate should be close to 0.5. Similarly, the average reward rate should correspond to the average probability value: (1+0.66+0.33+0)/4=0.5. As shown in Figure 4(b), our simulations results are consistent with these predictions and in the absence of learning, the GC and reward rates are both close to 0.5. The symmetry breaking events onsets are effective when a 40 Hz average firing rate difference is detected between two subpopulations. Figure 4 shows an example of a decision making (cognitive level) preceding an action selection (motor level) by 50 ms. For practical reasons symmetry breaking delays are computed from the smoothed firing rate curves difference. A 100 ms sliding window averaging convolution was applied. Changing the window size only slightly shifts the action selection times but the relative delays between cognitive and motor threshold onsets as well as the event orders are not affected. When the base current is too low, there is not enough gain in the BG direct pathway loops to destabilize their relative activities and no salience takes place between the motor cortex subpopulations. When it is too high, it tends to exceed its external inputs and therefore to drive the whole network activity in a balanced way which prevents symmetry breaking [Fig. 5(b)]. As with the noise level, there appears to be an optimum value to apply which is close to 100 pA.

Sensitivity study

We have then chosen these intermediate values of 50 pA for the noise and 100 pA for the base current in order (i) to maximize the network symmetry breaking performances but also (ii) to provide average firing rates consistent with those recorded in the different regions in vivo.

Lesion studies

Simulations have been performed to test the impact of lesions at each point in the circuit on network regions activity. 30 sessions were run on 8 different networks in four conditions. For each condition a given interconnection was selectively interrupted (synaptic weights set to 0) and the activities of different regions were recorded, pooled and averaged. The conditions used were control (intact) model, striato-pallidal lesion, cortico-thalamic lesion and pallido-thalamic lesion. The results are summarized in Fig. 6.

The striato-pallidal (direct pathway) lesion initially increases the GPi activity but rapidly, this increase inhibits in turn the thalamus and therefore the cortical sub-regions. Since the model activity is mainly driven by the cortex, the net effect of this lesion is then a global decrease in all subregions average firing rates.

Figure 6: Effect of selective lesions on the network populations average firing rates (Hz) recorded in 8 different networks over 30 sessions. c X , m X and a X : respectively cognitive, motor and associative X population. The populations abbreviations are: ctx for the cortex, str for the striatum, stn for the sub-thalamic nucleus, gpi for the GPi and tha for the thalamus.

The cortico-thalamic lesion also generates a global attenuation of firing rates.

Since the cortical inputs are the main driving force of the network activity and since the cortico-thalamic pathway is a positive gain feedback loop, when this connection is removed, the only remaining input to the thalamus is the inhibitory GPi input. The spontaneous thalamic activity is then drastically reduced and consequently the cortical activity. Therefore, as with the striatopallidal lesion, the global network firing rate decreases.

The pallido-thalamic lesion is also a consistent qualitative control of the behavior of our model. When the inhibitory projections from the GPi to the thalamus are removed, the brake that was exerted on the thalamo-cortical structures is stopped. The mutual interaction between the thalamus and the cortex becomes then more efficient which leads to an increase in the cortical regions firing rates and therefore in all the network subpopulations.

Learning properties

The optimum cue shape direction was preferentially selected

During training our model learns to create a dynamic link between the cognitive and motor sensory components of a cue without having to resort to rewiring cortical motor projections. This can be seen from the profile of the learning curves of the model. Indeed, the average reward and GC rates gradually increase over the course of the session as shown in Fig. 7(d). As a result, both the GCs and the GDs are significantly improved during a standard learning session of the four-cue protocol [Fig. 7(a)]. The two-cue protocol produces similar results [Fig. 7(b)] and achieves an even higher success rate for GCs and GDs. This better performance can be explained by the larger difference in the respective P(R) of the two targets and by the resulting decrease in uncertainty. The greater the cognitive cortico-striatal weight, the higher the gain in that channel. This leads the channel with the higher cortico-striatal synaptic weights being consistently selected [Fig. 7(c)]. Simultaneously the hyperdirect pathways excite GPi regions, which selectively inhibit the thalamic inputs projecting to the cortical regions whose striatal projections have the lowest weights. Cutting the thalamo-cortical projections in the circuit stopped the symmetry breaking (data not shown) showing that it was due to the action selection properties of the network and not to the increased salience of one target.

The movement onset delay decreases with learning

The movement onset (which can be equated to reaction time) is defined as the time between the appearance of the two cues and the symmetry breaking in cortical motor subpopulations. With learning, the time for movement onset decreased (Figs. 8(a) and 8(b)]. This is in accordance with previous modeling studies [ [START_REF] Guthrie | Interaction between cognitive and motor cortico-basal ganglia loops during decision making: A computational study[END_REF] as well as with experimental results [START_REF] Piron | The globus pallidus pars interna in goal-oriented and routine behaviors: Resolving a long-standing paradox[END_REF].

Striatal LI plays an important role in model learning capability

The absence of LI (NLI condition) impairs both levels of the decision making process [Figs. 8(c) and 8(e)]. This tends to confirm its role in gain control [START_REF] Moyer | Lateral and feedforward inhibition suppress asynchronous activity in a large, biophysically-detailed computational model of the striatal network[END_REF].

NLI decreases the GC rate in a naïve network [Fig. . This effect can be partially attributed to a deficient action selection process that prevents the model from reaching its optimum decision making performance. Together, these findings show a possible role of LI in striatal information processing and consequently, in the learning process.

Reversal learning protocol

Reversal learning consists of an n-step training procedure where the subject has to adapt its behavior to gain reward after a contingency change. This method is often used to unravel neuropsychological mechanisms [START_REF] Dombrovski | Corticostriatothalamic reward prediction error signals and executive control in late-life depression[END_REF], Cools et al., 2002, Costa et al., 2015]. To assess our model learning characteristics, we have implemented a reversal learning protocol which is summarized in Table 2. Cue number C0 C1 C2 C3

Step 1 (120 trials) P(R)=0 P(R)=1/3 P(R)=2/3 P(R)=1

Step 2 (240 trials) P(R)=2/3 P(R)=1 P(R)=0 P(R)=1/3 Step 3 (240 trials) P(R)=0 P(R)=1/3 P(R)=2/3 P(R)=1

In step 2, the reward contingencies were changed and their new distribution was chosen to maintain an homogeneous P(R) difference for all cues of 2/3.

The model behavior is very similar to what has been observed experimentally [Xue et al., 2013, Morita andKawaguchi, 2015]. Each new step was followed by an adaptation of the model that successfully improved its score after several tens of trials [Figs. 9(a)-9(c)]. However, each new step is followed by a short period of time during which GC score drops down below its initial average 50% rate. This can be explained by the fact that, during these periods, the model spontaneously selects what it considers as a GC but with inverted P(R)

and thus, it temporarily decreases its reward rate and therefore its learning rate. This process can also be visualized through the cortico-striatal cognitive projection strength evolution [Fig. 9(b)]. In summary it takes more trials to reach an optimum GC rate after each reversal learning step.

Extinction protocol

The extinction phenomenon is a common feature of most of the associative learning processes [START_REF] Barker | A unifying model of the role of the infralimbic cortex in extinction and habits[END_REF]. We have applied to the model a simple response extinction protocol [Goodman andPackard, 2015, Papachristou et al., 2013] which comprised the same training procedure as before, followed by the cessation of reward during 120 additional trials.

We observed that the GC performance gradually decreased [Fig. 10(a)] and exhibited statistically significant differences before and after extinction We also tested the model behavior when a recall was applied. Experimentally, the conditional response to a cue recall following a learning extinction is faster than the in the initial condition [Bouton, 2004] and this phenomenon is even observed in invertebrates [START_REF] Sandoz | Spontaneous recovery after extinction of the conditioned proboscis extension response in the honeybee[END_REF]. As shown in Figs.

10(c) and 10(d) our model was not able to exhibit this property. We can observe a memory effect if the extinction phase is not too long but the recall itself is not occurring faster.

Discussion

Following the flow of information

We have demonstrated that a large-scale, neuron level model of BG circuitry could be implemented with reasonable computation power and was capable of making action selections in complex behavioral tasks. At this point of the discussion, the question usually comes up: why using a spike-based approach instead of a rate-based approach?

The question remains open to decide whether or not, population rate-models can reliably mimic the true dynamics emerging of neural units interactions. This formalism is undeniably helpful when one tries to link large neuronal assemblies to behavioral observations. Yet, if we accept as true that the behavior of a system emerges from the interactions of its fundamental processing units, the model has sooner or later to be downscaled to this level to provide a more faithful and reliable description. This point has been very often discussed in the past and is still a matter of debate [Brette, 2015] but it seems that individual or relative spike-timing plays a major role in neural information encoding in different ways [START_REF] Portelli | Rank order coding: a retinal information decoding strategy revealed by large-scale multielectrode array retinal recordings[END_REF], Jacobs et al., 2009, Saal et al., 2015, Moyer et al., 2014]. Models relying on individual spiking neurons and of which construction is constrained by anatomical and physiological evidence of complex connectivity architectures often provide fruitful results because they directly link a detailed circuitry to its assumed function or behavior [START_REF] Chersi | A spiking neuron model of the cortico-basal ganglia circuits for goal-directed and habitual action learning[END_REF], Mandali et al., 2015, Medina et al., 2001, Yang et al., 2015].

Comparison of action selection mechanisms

Action selection requires that, of multiple alternatives presented, only one is chosen. This requires the use of a winner-takes-all architecture which usually relies on two different mechanisms. The first mechanism (i) relies on the feedback properties of the network itself. Our model is based on the presence of two feedback pathways having opposite effects and passing from cortex through the BG and back to cortex. On the basis of previous studies [Mink, 1996, Leblois et al., 2006a, Guthrie et al., 2013] we implemented a schematic BG action selection model in which, separate cortical networks of individual neurons are activated for each of a set of possible actions. In the model, the hyperdirect pathway negative feedback imposes its global inhibitory effect on cortical subregions. In parallel, the direct pathway exerts a more localized disinhibition which is gradually amplified and leads to the selection of an action.

The second type of mechanism (ii) involves LI. This property has been observed in the striatum where domains of mutually inhibitory connections have been reported [Oorschot, 1996]. Many computational models have also explicitly used LI to produce "winner takes all" action selection networks involving competition mechanisms [START_REF] Bar-Gad | Stepping out of the box: information processing in the neural networks of the basal ganglia[END_REF], Suri and Schultz, 1999, Alexander and Wickens, 1993, Groves, 1983, Kotter and Wickens, 1998, Woodward et al., 1995, Wickens and Arbuthnott, 1993]. Even if recurrent inhibition is often considered as weak compared to feedforward inhibition [START_REF] Jaeger | Surround inhibition among projection neurons is weak or nonexistent in the rat neostriatum[END_REF], Koos et al., 2004, Tunstall et al., 2002], it has recently been emphasized that its role had to be considered [START_REF] Moyer | Lateral and feedforward inhibition suppress asynchronous activity in a large, biophysically-detailed computational model of the striatal network[END_REF] and our simulations have shown its positive effect on learning capabilities of the BG.

Two-level action selection

Previous models of BG [START_REF] Gurney | A computational model of action selection in the basal ganglia. i. a new functional anatomy[END_REF][START_REF] Leblois | Temporal and spatial alterations in gpi neuronal encoding might contribute to slow down movement in parkinsonian monkeys[END_REF] have implemented selection between two choices at one level. In the current study, the presented cue is separated into two types of sensory stimulus (levels): the cue shape and its position [cf. Fig. 3(b)]. Under this interpretation, the action selection then requires two choices, one of the cue shape (cognitive component)

and the other of the direction (motor component) which are implemented in parallel. This two-level decision making process was initially foreseen in a previous experimental study [START_REF] Pasquereau | Shaping of motor responses by incentive values through the basal ganglia[END_REF]. A first implementation relying on population rate-models and mathematical transfer function was then developed in [START_REF] Guthrie | Interaction between cognitive and motor cortico-basal ganglia loops during decision making: A computational study[END_REF] where anatomical evidences for its underlying architecture were also presented. In this study, the divergence in the cortical activations of cognitive and motor subpopulations was described as an emergent property of the network. The present model still performs the previously observed two-level action selection process and its related learning properties but, including additional circuitry elements and using a more detailed formalism, it extends this capability to new protocols and situations.

Learning in the network

In the naïve state, the network is able to spontaneously perform action selection.

SB results from its connectivity pattern and intrinsic noise. Since no initial prewiring is present for any of the four-cue (or two-cue) protocol, GC and GD rates are close to 50% [Figs. 7(a) and 7(b)). The reinforcement learning process which takes place during a training session results from the synaptic weight changes of the cognitive cortex projections toward striatum and is modulated by the phasic variations in dopamine concentrations which have been shown to be necessary both for the LTP and for the LTD [START_REF] Pawlak | Dopamine receptor activation is required for corticostriatal spike-timing dependent plasticity[END_REF], Kerr and Wickens, 2001, Reynolds et al., 2001]. Our model predicts efficiently the experimental observations of the four-cue and two-cue tasks [START_REF] Pasquereau | Shaping of motor responses by incentive values through the basal ganglia[END_REF], Piron et al., 2016].

Its learning properties also exhibit consistent dynamics when submitted to reversal learning and extinction protocols. However, it also shows its limitation on these occasions. Indeed, during the reversal learning protocol, it fails to switch quicker to a new configuration as it is experimentally reported [START_REF] Costa | Reversal learning and dopamine: a bayesian perspective[END_REF]. Similarly, during the extinction protocol, it does not exhibit a faster recall. These limitations do not necessarily throw doubt over the consistency of the model. They just highlight the fact that other important regions are not explicitly included in the model like the hippocampus which is involved in reversal learning [START_REF] Shohamy | Distinct hippocampal and basal ganglia contributions to probabilistic learning and reversal[END_REF] and the amygdala which is also known to play an important role in extinction process [START_REF] Lingawi | Amyg-dala central nucleus interacts with dorsolateral striatum to regulate the acquisition of habits[END_REF].

Conclusion

We have presented here, for the first time, a biophysically based, spiking neuron model of the BG that is able to perform action selection explicitly relying on the interaction between the cognitive and motor levels. This model is closely based on the known anatomy and physiology of the BG and illustrates a reasonable network mechanism of decision making. In addition, it confirms that the action selection can be driven by noise, but that simulated learning can overcome this noise to produce optimum action selection performances [START_REF] Guthrie | Interaction between cognitive and motor cortico-basal ganglia loops during decision making: A computational study[END_REF]. Our model bridges the gap between top-down mesoscopic approaches and bottom-up models relying on emerging properties of neuronal networks dynamics. It is also able to predict some important behavioral characteristics like localized lesion effect on learning, reversal learning and extinction protocol.

Figure 1 :

 1 Figure 1: Box and arrow diagram of the cortico-basal ganglia network and pathways, based on [[START_REF] Bar-Gad | Information processing, dimensionality reduction and reinforcement learning in the basal ganglia[END_REF], Moyer et al., 2014].

Figure 2 :

 2 Figure 2: (Color online) Detailed architecture of the 72 regions of the model. The cortico-basal ganglia loops are described taking into account the two levels of decision making: (i) a cognitive loop (blue subpopulations) and (ii) a motor loop (pale red subpopulations). The cortical and striatal associative regions are in green. Each cell of the grid (for instance M1 or C3) represents a neuronal subpopulation which size depends on the region. A partial connectivity template taking into account M3 and A4 cortical inputs is shown here (for the sake of clarity the complete connectivity pattern is not shown). The plastic synapses considered in the model exclusively arise from the cognitive (magenta frame) cortico-striatal projections. The central part of the figure represents the hyper-direct pathway (cortex -STN -GPi) whereas the right side represents the direct pathway (cortex -striatum -GPi).

Figure 3 :

 3 Figure 3: (Color online) (a) Average neuronal firing rates (Hz) pooled from 30 different networks recorded over 30 trials of 1 s each (N = 30; p < 0 : 05; one -wayAN OV A). Error bars represent standard deviation of the pooled data. (b) Combination sample of displayed targets during the task with their shape/color and localization on the screen and (c) encoding of the target presentation in the corresponding cortical subpopulations (yellow for motor, black for associative and dark blue and red for the two cognitive subregions).

Figure 3 (

 3 b) shows a combination composed of M2-C2 for target 1 (blue triangle) and M1-C3 for target 2 (red cross). This configuration is encoded in the model by the stimulation of the corresponding framed subpopulations [cf. Fig. 3(c)]. The firing rates recorded in the various cognitive, associative and motor subpopulations remains globally

Figure 4 :

 4 Figure 4: (a) Recording of the average firing rate in the subpopulations M0, M3, C1 and C3 following the simultaneous presentation of the target C3 at the M0 location and of the target C1 at the M3 location. This trial illustrates a GC example since the selected motor activity is M0 which corresponds to the direction of the presentation of the shape C3 which has the highest P(R). (b) Average percentage of reward and GC rates in 16 sessions of 100 trials. Both scores are consistent with 50% chance (N = 16; p < 0 : 05; two-sided Wilcoxon test).

2. 3 . 1

 31 Effect of noise and base current on symmetry breaking in the model Both noise and base current amplitude [cf. (refsec:implementation)] affect the network ability to generate symmetry breaking. As shown in Fig. 5(a), setting noise amplitude too low or too high decreases its symmetry breaking score in the motor cortex (i.e, its action selection capability) and the optimum noise level of our model is close to 50 pA.

Figure 5 :

 5 Figure 5: Effect of ξ(t) (current noise amplitude) and (b) basal input current on the percentage of symmetry breaking in the motor cortex (SB) following the presentation of two random targets at two different positions (N = 16; p < 0 : 05, Kruskal-Nemenyi multiple comparison test).

Figure 7 :

 7 Figure7: Effect of learning on model behavioral metrics in (a) four-cue protocol and (b) two-cue protocol, "before" refers to the first 30 trials of a session and "after" to the last 30 trials (N = 16; p < 0.05;Wilcoxon test). (c) change in average cognitive cortico-striatal synaptic weights during a training session. w i is the average weight for cue i . In these simulations, the higher the index number (i), the higher the associated cue reward probability (P i=0 (R) = 0, P i=1 (R) = 0.33, P i=2 (R) = 0.66, P i=3 (R) = 1). (d) Normalized rate of GC and rewards averaged over 24 sessions of the four-cue protocol. The smoothed curves are obtained by a local polynomial regression fitting combined with a 95% confidence interval.

  8(c)-left] and abolishes its learning capability (Fig. 8(c)-right]. This latter result seems related to the more general fall of the symmetry breaking score shown in Fig. 8(d). NLI condition

Figure 8 :

 8 Figure 8: Top: average movement onset delay is decreased by learning in (a) fourcue protocol and (b) two-cue protocol, "before" refers to the first 30 trials of a session and "after" to the last 30 trials (N = 16; p < 0 : 05;Wilcoxon test), Bottom: effect of striatal LI (or its absence NLI) on learning performances of the model (c) GC score significantly differs both before and after learning when LI is absent (d) the NLI condition dramatically decreases the number of SB motor events. This indicates that a motor selection occurs less frequently both before and after learning (e) after learning GD score depends on LI (N = 16; p < 0 : 05;Wilcoxon test).

[

  . This occurred in parallel with the cortico-striatal weights variation over time[Fig. 10(b)]. The GC profile is consistent with the general extinction process as described in classical conditioning context. Indeed when it is deprived from reward, the model spontaneously loses its capacity to optimize its choices and gradually "forgot" what it learnt.

Figure 9 :

 9 Figure 9: (Color online) 3-step reversal learning protocol simulation results (a) Normalized rates of GC averaged on 16 sessions (red: smoothed curve obtained by a local polynomial regression fitting combined with a 95% confidence interval). To compare the efficiency of reversal learning 30 trials samples (color boxes) were analyzed at the beginning and at the end of the three steps (GCBi: good choice before step i and GCAi: good choice rate after step i) (b) variation of average cortico-striatal cognitive synaptic weights over a training session. w i is the average weight value for each of the four cues. (c) GC rate comparison before and after training at each step (N = 16; p < 0 : 05, Kruskal-Nemenyi multiple comparison test).

Figure 10 :

 10 Figure 10: (Color online) Extinction protocol simulation results (a) Normalized rates of GC averaged on 16 sessions during the single extinction protocol (red: smoothed curve obtained by a local polynomial regression fitting combined with a 95% confidence interval). (A-inset) comparison of GC scores averaged on 30 trials samples (color boxes) recorded (1) at the beginning, (2) before extinction and (3) after extinction (N = 16; p < 0 : 05, Kruskal-Nemenyi multiple comparison test). (b) variation of average cortico-striatal cognitive synaptic weights over time. w i is the average weight value for each of the four cues. The extinction starts at 120 trials (orange marker), (c) Normalized rates of GC averaged on 16 sessions during a single extinction protocol followed by a recall. (d) variation of average cortico-striatal cognitive synaptic weights over time. The extinction starts at 120 trials (orange marker) and ends at 180 trials (recall: green marker).

Table 2 :

 2 Reversal protocol description.

Acknowledgments

The authors want to thank Eman KHEDR (Neurology Department, Faculty of Medicine, Assiut University, Assiut, EGYPT) and the NEUROMED project, funded by the Capacities Programme in the European Union's 7th Framework Programme (FP7-REGPOT-245807).

Martin Guthrie and André Garenne contributed equally to this paper.


Abdel Nasser Tigrine

Zohra Bellahsene

Konstantin Todorov

Selecting Optimal Background Knowledge Sources for the Ontology Matching Task

It is a common practice to rely on background knowledge (BK) in order to assist and improve the ontology matching process. The choice of an appropriate source of background knowledge for a given matching task, however, remains a vastly unexplored question. In the current paper, we propose an automatic BK selection approach that does not depend on an initial direct matching, can handle multilingualism and is domain independent. The approach is based on the construction of an index for a set of BK candidates. The couple of ontologies to be aligned is modeled as a query with respect to the indexed BK sources and the best candidate is selected by following an information retrieval paradigm. We evaluate our system in a series of experiments in both general-purpose and domain-specific matching scenarios. The results show that our approach is capable of selecting the BK that provides the best alignment quality with respect to a given reference alignment for each of the considered matching tasks.

Introduction

Over the past years, the web has been continuously evolving from a web of documents to a web of data, following the principles of data and knowledge representation, publishing and linking. The Linked Open Data project1 , the web of data most successful initiative to date, comprises nowadays hundreds of datasets over several domains of life and science. While information is expressed by the help of RDF (Resource Description Framework) statements, knowledge about the domains of interest is given in the form of ontologies, which provide common vocabularies to name classes of things (concepts) and relations between these classes, defining in an explicit manner their semantics. Ontologies, expressed in RDFS or OWL, can be simple sets of terms, thesauri or more complex structured vocabularies with logical expressions that allow for the inference of new facts.

It occurs often that ontologies, describing similar or equivalent domains of knowledge, are expressed differently. These differences, referred to as ontology heterogeneities, can occur in terms of terminology (choosing different names to refer to the same concepts and relations), structure or semantics (relating classes in different ways, giving different intensions to information) or simply in terms of syntax (choosing different formal representations). In order to unlock the potential of the web of data and foster the creation of a veritable information network, heterogeneous ontologies have to be linked together by explicitly declaring the equivalence relations between their entities (classes and properties). The field of ontology matching has taken the challenge of proposing solutions that allow to automatically discover the correspondence between ontological elements in the presence of one or more of the heterogeneities cited above. As a result of almost 20 years of research and practice, many approaches and systems exist, capable of aligning highly heterogeneous ontologies [START_REF] Shvaiko | Ontology matching: state of the art and future challenges[END_REF].

It has been shown in recent publications [START_REF] Faria | The agreementmakerlight ontology matching system[END_REF][START_REF] Tigrine | Light-weight cross-lingual ontology matching with LYAM++[END_REF] that the ontology matching process can benefit largely from the use of Background Knowledge (BK). BK is understood as any external reference knowledge that can facilitate the matching process, given in the form of large general purpose ontologies or well-established knowledge graphs (such as DBPedia or YAGO), domain specific ontologies, or the web at large. We outline three main advantages of the use of BK when aligning ontologies. In the first place, as observed by [START_REF] Sabou | Exploring the semantic web as background knowledge for ontology matching[END_REF], there is always an inherent semantic gap between two ontologies, coming from the missing semantic context of their acquisition. BK can help close that gap, as shown in [START_REF] Todorov | Fuzzy and cross-lingual ontology matching mediated by background knowledge[END_REF]. In the second place, and even more importantly, the ontology matching process is heavy and costly: most of the existing matching tools are complex engineering artefacts comprising a sophisticatedly orchestrated pipeline of matching modules, mapping filtering and semantic verification components. In a recent study [START_REF] Tigrine | Light-weight cross-lingual ontology matching with LYAM++[END_REF], we have shown that an appropriately chosen BK source can help significantly lighten the overall matching process. Finally, in specific domains there is a clear need for specific reference knowledge, since the commonly used external knowledge sources, such as WordNet, fail to provide the semantic information that is needed to discover correctly the correspondences between domain specific concepts.

While there is little doubt about the benefits of using BK for ontology matching, outlined as one of the challenges for the field by [START_REF] Shvaiko | Ontology matching: state of the art and future challenges[END_REF], an important question remains largely unanswered: how to select an optimal BK source for a given ontology matching task out of a set of known BK sources? We understand "optimal" as the source that provides the best quality of the alignment produced for two ontologies. In this paper, we attempt to answer this question by proposing an approach for the automatic selection of a BK source for a given ontology matching task. We situate the problem in an information retrieval framework. The set of known BKs is indexed by using the well-known vector space model while the two ontologies to be aligned are represented as a query document. The comparison between the ontologies and the BKs is based on their content, but also on their structure. We elaborate on the different choices of a similarity measure for this task. Particularly, we show that the commonly used cosine similarity is not the best choice in this scenario and we propose the use of correlation-based similarity measures. The selection system that implements this approach has the properties of being fully automatic, domain independent and multilingual, as well as being entirely dissociated from the alignment process.

In order to evaluate the proposed approach, we carry out experiments on benchmark data coming from the ontology alignment evaluation initiative (OAEI). We used as background knowledge sources a mixed set of domain specific and general purpose knowledge graphs. The results show that our approach guarantees the selection of the optimal BK source with respect to each of the matching tasks that has been performed in terms of the quality of the produced alignment by using the selected BK.

The paper is structured as follows. The following section introduces the BK selection problem by focusing on requirements and criteria for selection. Section 3 describes our approach that we support experimentally in Section 4. Several related results are discussed and compared to our method in Section 5 before we conclude in Section 6.

The Background Knowledge Selection Problem

Ontology matching is the process of automatically discovering semantic correspondences between the entities of two ontologies that are assumed to cover overlapping domains of knowledge. The result of the ontology matching process is a set of pairs of cross-ontology entities (names of concepts or properties) called an alignment, where the entities of each pair are bound by a given semantic relation (most commonly equivalence) [START_REF] Ngo | Opening the black box of ontology matching[END_REF].

As pointed out in the introduction, using an appropriate background knowledge source (hereafter, BK for short) in the matching process can help improve the results by potentially decreasing the complexity of the process. A BK is understood as any piece of external information that can be used in order to improve the matching quality. According to [START_REF] Shvaiko | Ontology matching: state of the art and future challenges[END_REF], one can consider as BK for ontology matching a large range of external sources, such as linked data, domain specific corpora of schema and alignments, domain specific or general purpose ontologies, dictionaries and thesauri, lexical databases. Since, on the one hand, the choice of BK has a direct impact on the results and, on the other hand,there is a multitude of available BK sources, researchers in the field have recognized the need for an approach to select automatically the optimal BK for a given matching task.

Criterium of Optimality of a BK

There is a large set of BK sources that can be considered, some of them not even known to the user. For that reason, it is important to frame formally the criterium that defines an optimal BK. Since the aim of using a BK is to provide good quality matching results no matter the provenance and nature of the BK, its choice has to be motivated by the maximization of the alignment quality. Suppose that for a given matching task (a pair of ontologies to be aligned). The best BK for this matching task, that we call optimal BK, is selected as the one that produces the best alignment.

Let Γ = {BK 1 , ..., BK n } be a set of known BKs. Let s, t be two ontologies (s for source and t for target) and A = {A 1 , ..., A n } -a set of alignments of s and t each using a different BK from Γ , given as A i = (s, t, m i , BK i ), where A i is produced by using BK i , m i is the metric selection value between (s, t) and BK i , ∀i = 1, ..., n.

Definition 1 (Optimal BK). We define the optimal background knowledge source for the task of matching s and t as the background knowledge source BK o ∈ Γ , which corresponds to an alignment from A with the higher quality. In case multiple BKs produce alignments with maximal m i values, the one with the lowest number of entities is defined as optimal.

The optimality criterium given above is inherently semantic, although this remains implicit in the definition. The BK-based ontology matching systems are designed in such manner that the BK that maximizes the quality an alignment of two ontologies is the one that is closest in content to these ontologies. This is the reason why our selection method is based on content similarity between the BK sources and the input ontologies. In our experiments, we show that a BK selected by the help of this method is optimal in the sense of definition 1 (see Section 4).

As a final remark, note that we do not base the selection criterium on the improvement provided by a BK as compared to a direct matching. Our assumption is that an user is looking for a BK because she is not satisfied with the results achieved by a direct matching.

Requirements to an Automatic BK Selection System

We outline the requirements that, in our view, a BK selection system has to meet.

BK type independence. The system has to be able to take into account

BKs serialized differently (SKOS, OWL, ttl, etc.) as long as there exists a parser able to extract the textual information and structure from the BKs and of different semantic nature (thesauri, ontologies, lexical databases, corpora). 2. Domain independence. The system should be able to propose a BK for a pair of ontologies of any given domain of knowledge. 3. Multilingualism. The system has to be able to select a BK that assists the alignment of cross-lingual ontologies. 4. Optimality. It should be guaranteed that the system returns an optimal BK with respect to a matching task in the sense of definition 1. to be aligned -as a query document in the form of a set of terms. The corpus Γ is indexed in order to represent its content by using standard information retrieval techniques, that we explain further on. One of the particularities of our approach consists in the fact that we construct a common index for all known BKs, independent on their domain and focus. As we shall see, in this way we reply to the first two requirements given in the previous section. Additionally, the effort of indexing large ontologies is performed only once, which contributes to the efficiency of the approach. Note also, that the query is given in the form of a unique document representing the pair of ontologies (and not one document per ontology), because we want to retrieve the background knowledge that is common for the two and therefore allows for their reconciliation. In the following, we first explain on how we transform the BK sources and the query ontologies to documents. Then we describe the indexing process and present a set of similarity measures that we use in our approach for retrieving the optimal BK for a given matching task. The overall process is depicted in Figure 1.

Modeling Ontologies and BKs as Structure-Content Documents

We map a BK source to a text document that we call a BK-document in a manner that allows for taking into account both the content and the structure of the knowledge sources into account. The term extraction method consists in the following. Each token of the labels of the concepts of a given BK becomes a term in the corresponding BK-document. In order to preserve the information relevant to the BK structure, we add a given term to the BK-document every time when it appears in a label of a sub-class or a superclass within the BK hierarchy or, when it appears in the label of a concept in the domain or the range of a property or, more generally speaking, when it appears in the label of a concept of any relation (synonymy, subsumption, etc).

To illustrate this idea, take a part of a BK where the classes {Author, Administrator, PhD Student, Professor} are all in a subclassOf relation with the class Person. Without the use of the structure, the resulting BK-document would be d BK = {Person, Author, Administrator, PhdStudent, Professor} with all the terms having the same weight with respect to their frequency of occurrence. However, the term Person seems to be more important than the other terms in the BK as it is a label of their common superclass. Not considering this semantic information affects considerably the computation of weights in the indexing phase. By using the structural information, the BK-document becomes d BK ={Person, Person, Person, Person, Person, Author, Administrator, PhDStudent, Professor}.

We model in this manner all known BKs in Γ , resulting in the corpus D Γ = {d BK1 , d BK2 , ..., d BKn }. We proceed in the same manner in order to represent a pair of ontologies, t and s, as a query document, denoted by q t,s by creating a document for each ontology as shown above and then merging the two documents into a single one.

Indexation

Prior to indexing, we apply a standard set of text preprocessing methods, such as normalization of characters and spaces, removing diacritics or accents, deleting numbers, punctuations and stop words, tokenization and lemmatization.

We index the documents in D Γ by using the well-known vector model. We build an indexation matrix M , which has BK-document vectors as rows and index term vectors as columns. Standardly, the index terms are the terms collected from the BK-documents without repetition after preprocessing. We denote the set of index terms by C t . Each element w ij of M corresponds to the weight of the term t j with respect to d BKi .

In order to compute the weights w ij , we use the well-known TF-IDF (Term Frequency-Inverse Document Frequency) weighting scheme that captures the importance of a term both within a single document and in a collection of documents. For a term t j and a BK-document d BKi , the weight w ij is calculated as follows:

w ij = tf (t j , d BKi ) * log( n df (t j ) ), (1)
where tf (t j , d BKi ) is the frequency of occurrence of the term t j in the document d BKi and df (t j ) is the number of documents containing t j and n is the number of documents in D Γ .

Retrieving the Optimal BK

We need a similarity measure of some kind, which allows the system to return to the user the BK with highest similarity to the input ontologies query.

In information retrieval, the most commonly applied similarity measure is the cosine similarity, denoted by cosine, given as the normalized dot product of two document vectors. We noticed that in certain cases parameter free measures of (rank) correlation can be applied more successfully than the cosine similarity measure for our particular problem. A measure of correlation expresses the degree of dependence of two random variables. It takes values between -1 and 1, assuming strong correlations for high positive values, strong anti-correlations for high negative values and no dependence for values close to 0. We introduce two of the most popular choices for correlation measures and show how they can serve as similarity measures for two documents [START_REF] Conover | Practical Nonparametric Statistics[END_REF]. Note that the correlation measures to be presented, just as the cosine measure, are based on the dot product of vectors. In that sense, the cosine similarity can be seen as a correlation, just as the correlations can be seen as similarity measures.

Pearson Correlation. The Pearson's coefficient r between two variables X and Y is calculated from their covariance cov X,Y and their standard deviations σ X and σ Y in the following way:

r X,Y = cov X,Y σ X * σ Y = i (x i -m X )(y i -m Y ) i (x i -m X ) 2 i (y i -m Y ) 2 , (2)
where m X and m Y are the means of X and Y .

In our case, each of the variables X and Y corresponds to either a BKdocument or a query document that all live in the same space and are therefore representable by the same type and number of features (i in [START_REF] Faria | The agreementmakerlight ontology matching system[END_REF] takes values from 1 to the number of index features). The sets of values {x i } and {y i } correspond to the values of the tf * idf vectors in our vector model. Pearson is used to test the linear dependency of variables.

Spearman Correlation. Spearman's coefficient provides a measure of the correlation of two variables X and Y represented as lists of statistical rankings. In contrast to Pearson, it is applied when a general monotonic relationship is expected between the variables. Formally, it is given as

ρ s = 1 - 6 i d 2 i n 3 -n , (3)
where d i is the difference between the rank of the ith observation of the variable X and the rank of ith observation of the variable Y ,

d i = rank(x i ) -rank(y i ).
We transform the tf * idf values to ranks by using the partial order on real numbers. In case of equal values, we assign equal ranks.

BK Selection. For a given corpus of indexed BK-documents D Γ , a query q s,t and a similarity measure σ ∈ {cosine, r, ρ s }, the selected BK is the one whose BK-document maximizes the similarity between the query and the documents in D Γ , given as

D BKs,t = arg max D BK ∈D Γ σ(D BK , q s,t ). (4)
In case more than one BKs provide a maximal similarity to the query, the one with lowest number of entities is selected.

In case where an ontology matching system uses more than one BK at a time, we can recommend the top-K BKs, with respect to their similarity to the input ontologies. These sources can be further combined -a problem that is not addressed in this paper.

Where no optimal BK is found in the set of BKs, we can easily apply threshold limits to avoid this scenario. In our study, we have considered that always an optimal BK exist in the set of BKs.

We show experimentally in Section 4 that the selected background knowledge source BK s,t corresponding to the BK-document D BKs,t is optimal in the sense of definition 1.

Evaluation and Results

In order to evaluate our approach, we have conducted experiments on data coming from the ontology alignment evaluation initiative (OAEI)2 of year 2015. Our aim is to test if our approach selects the optimal BK among a set of BK sources in two scenarios: selecting a domain specific BK or selecting a general purpose BK. We take a set of BKs Γ = {Yago, DBpedia, BabelNet, DBnary, FMA, Doid, Uberon}, described below. The set Γ includes general purpose sources (Yago, DBpedia, BabelNet and DBnary), as well as several domain specific anatomy and biomedical BKs (FMA, Doid, Uberon).

As described in Section 3, the selected BK for each task has to conform to the optimality criterium given in Definition 1. In order to verify this criterium, we need a F-measure score produced as a result of the comparison of an alignment given by an ontology matching system that uses BK in its process and a reference alignment. For the totality of our experiments, we have used the system LYAM++ [START_REF] Tigrine | Light-weight cross-lingual ontology matching with LYAM++[END_REF], which is entirely based on BK and has also shown to perform well on the OAEI MultiFarm track on which it participated last year [START_REF] Tigrine | Lyam++ results for oaei 2015[END_REF]. LYAM++ don't use any complex matching methods regard to the BK. For instance, LYAM++ use HasSynonyms relation presented in given BK to match between two concepts.

Note again that the aim of these experiments is not to show the quality of the ontology matching tools, but to evaluate the performance of the BK-selection approach proposed in this paper. The pairs of ontologies to be aligned, as well as the BKs in Γ are modeled as documents and indexed as described in the previous section. In the retrieval phase, we have tested the performance of the three similarity measures given in Section 3 -the commonly used cosine similarity and the two parameter-free correlation coefficients (Pearson and Spearman).

The OAEI tracks

The Anatomy track aims at discovering alignments between a human anatomy ontology, part of the NCI Thesaurus3 and a mouse anatomy ontology. This track is considered as a large-scale matching task because the input ontologies are of a large size and very rich semantically. The Large Biomedical track aims at aligning three large bio-medical ontologies, namely FMA, SNOMED and the NCI Thesaurus. Since FMA appears in a query couple, we did not consider this ontology as background knowledge source for this track. The Anatomy and the Large biomedical tracks have been selected to make sure that at each experiment our approach selects from Γ the right BK for the right domain, respectively anatomy and biomedicine.

The Conference track contains a dataset of about 15 ontologies from the scientific publication field, together with reference alignments. We have used with the Conference dataset to test if the approach selects the optimal general purpose BK among the mixed set of BKs Γ . Note that, although the Conference data are specific to the scientific publishing domain, they can be considered as general purpose due to the type of concepts that are used to describe this domain, often dealing with common sense knowledge.

Finally, the MultiFarm track is derived from the Conference track data by translating the conference ontologies into several different languages with the aim to challenge the performance of cross-lingual ontology matching tools. In our scenario, this track is appropriate for testing whether the selection procedure is able of choosing an optimal multilingual knowledge source for aligning crosslingual ontologies.

BK sources

We give a quick overview of the BK sources used in this evaluation. Babel-Net [START_REF] Navigli | Babelnet: The automatic construction, evaluation and application of a wide-coverage multilingual semantic network[END_REF] is a multi-lingual semantic network and an ontology that has been built by merging different encyclopedic and linguistic resources. The integration of these resources has been conducted automatically. BabelNet appears to be an appropriate choice of a BK for the MultiFarm track. DBnary4 [START_REF] Sérasset | Dbnary: Wiktionary as a lemon-based multilingual lexical resource in RDF[END_REF] is a multilingual lexical database extracted from Wiktionary, which is also a potentially good candidate for the MultiFarm track. DBpedia [START_REF] Auer | Dbpedia: A nucleus for a web of open data[END_REF] is a large multilingual knowledge graph extracted from Wikipedia, covering a multitude of areas such as music, films, people, places, etc.. YAGO [START_REF] Suchanek | Yago: a core of semantic knowledge[END_REF] (Yet Another Great Ontology) is a another large multilingual general purpose knowledge graph extracted from Wikipedia, GeoNames 5 and WordNet. Both YAGO and DBpedia can be considered as candidates for a large variety of general purpose ontology matching tasks. Doid 6 is an open source ontology for the integration of biomedical data associated with human diseases. In our evaluation setting, Doid can be potentially used for aligning Biomedical or Anatomy-related ontologies. FMA (Foundational Model of Anatomy) [START_REF] Rosse | A reference ontology for biomedical informatics: the foundational model of anatomy[END_REF] is the reference ontology for the anatomy field. Similarity, Uberon [START_REF] Haendel | Unification of multi-species vertebrate anatomy ontologies for comparative biology in uberon[END_REF] is a multi-species anatomy ontology. Both ontologies can be used for the Anatomy ontology matching task. The results from this series of experiments are presented in Tables 1 and2. For each BK, we provide the average similarity scores obtained by each of the three similarity measures described in Section 3 and the corresponding average F-measure values obtained in the BK-based alignment. The average values are computed over all pairs of ontologies in each track. The best score achieved by each similarity measure, as well as the highest F-measure value are highlighted. The two correlation coefficients take values in the [-1, 1], which explains the negative numbers. We are interested in strong correlations, corresponding to high similarity. Recall that according to our criterium, the BK selected by a similarity measure is optimal if it guarantees the highest F-measure.

Results Analysis

As it can be seen from the results in Tables 1 and2, our approach systematically selects the optimal BK, independently on the track, by using the Spearman correlation and very conclusively so with similarity scores around and above 0.5. The performance of the selection method is flawed when using the cosine similarity, which is the common choice for a similarity measure in an information retrieval setting, but ranks only second best in our experiments. Namely, it fails to detect the optimal BK on the Anatomy and the Conference tracks and on the other tracks its outcome does not always help to come up with a clear cut decision.

We explain this observation by the fact that the Spearman measure is based on ranks instead of real values and on monotonic dependencies between the two vectors. Precisely, a small variation in the corresponding values of two vectors influences the cosine similarity negatively, while this is less so in case of Spearman. Spearman seems to be also better suited to dealing with highly sparse data (it is most of the times the case that the query document corresponding to two input ontologies contains much less terms than any of the BK-documents in the selection pool).

As for the Pearson correlation coefficient, Spearman appears to largely outperform that, as well. This is mainly due to the fact that the Pearson correlation measure is suited for testing linearity of the variables, while Spearman assumes monotonic behavior of the rank pairs. We draw the reader's attention to the fact on the Anatomy track Pearson yields a maximal value for two different BKs -Uberon and FMA. The BK selected by this measure is Uberon, the smaller of the two sources, conforming to our selection condition given at the end of Section 3. UBERON is well known as the perfect BK for anatomy task. However, if UBERON does not exist in the set of BKs the approach will select FMA as the optimal BK because FMA has the higher correlation value than the other BKs.

Finally, we note that the choice of a similarity measure is more important in the presence of multiple similar in terms of domains BKs, as this is the case in the OAEI experiments, where the only similarity measure that remains unflawed is Spearman.

Related Work

We provide an overview of related approaches to ontology matching with regard to two aspects of this task: (1) the use of background knowledge and (2) the automatic selection of background knowledge.

Ontology Matching Using Background Knowledge

The idea of using background knowledge (BK) for enhancing ontology matching task is not new and has been successfully adopted in several matching approaches. Although not directly relevant to our study, which focuses on the BK selection process, we summarize here the main groupes of relevant approaches.

An intuitive idea is to rely on reusing existing mappings in order to improve the mappings produced by a system. Several approaches [START_REF] Do | COMA -A system for flexible combination of schema matching approaches[END_REF][START_REF] Groß | GOMMA results for OAEI 2012[END_REF][START_REF] Saha | Schema covering: a step towards enabling reuse in information integration[END_REF] follow this paradigm. The main drawback of this group of methods is the fact that they depend heavily on the quality of the re-used mappings and, hence, on the performance of the ontology matching techniques that have been used to produce them.

Another approach consists in using a corpus, which can be seen as a rich collection of data elements and their data types, relationships between elements, sample data instances and other information that can be used to discover mappings between entities [START_REF] Madhavan | Corpusbased schema matching[END_REF][START_REF] Madhavan | Corpus-based schema matching[END_REF]. Furthermore, domain specific ontologies are often seen as quality sources of background knowledge. In [START_REF] Aleksovski | Matching unstructured vocabularies using a background ontology[END_REF][START_REF] Aleksovski | Exploiting the structure of background knowledge used in ontology matching[END_REF], the alignment process takes place in two steps: anchoring and driving relations. Anchoring consists in matching the concepts of the source and target ontologies to the concepts of the reference knowledge using standard ontology matching techniques. Relations between source and target concepts are derived by checking if their corresponding anchored concepts are related.

A group of approaches relies on the web in order to discover (by crawling) automatically relations between the input ontologies entities that may exist in various knowledge sources distributed on the web [START_REF] Sabou | Exploring the semantic web as background knowledge for ontology matching[END_REF].This is particularly useful when the needed background knowledge is spread among different sources. More recently, several approaches have been proposed that rely on general purpose knowledge graphs, such as Yago and DPBedia. It has been shown that such sources are particularly useful for aligning cross-lingual ontologies [START_REF] Todorov | Fuzzy and cross-lingual ontology matching mediated by background knowledge[END_REF][START_REF] Tigrine | Light-weight cross-lingual ontology matching with LYAM++[END_REF].

Automatic Selection of Background Knowledge

To the best of our knowledge, there are only a few approaches that have addressed the question of automatic BK selection.

In [START_REF] Faria | Automatic background knowledge selection for matching biomedical ontologies[END_REF], an automatic background knowledge selection approach has been proposed for the particular task of matching biomedical ontologies based on the notion of mappings gain (MG). MG is used to estimate the individual usefulness of background knowledge sources and is defined as a function of the improvement of the number of correct mappings by using a given BK source as compared to a direct mapping of two ontologies. The BK providing the highest MG is selected. The authors have shown experimentally the correlation between the mapping gain and the F-measure in most of the matching tasks that they perform. However, it seems that the notion of MG is not always reliable. Indeed, as reported by the authors, despite having a relatively high mapping gain, using a selected BK may have a negative impact on the results for some tasks; this is the case of using WordNet as BK. The main drawback of the approach is the fact that the selection procedure, defined by the concept of MG, depends on an already existing alignment between the source ontologies.

The closest to our work is reported in [START_REF] Quix | Automatic selection of background knowledge for ontology matching[END_REF]. In this approach, a local repository is built from a set of ontologies, to be used as background knowledge sources. These resources are indexed by extracting concept names, comments and labels. In addition and separately, structural features are taken into account. Querying the repository is performed for a given source and target ontology, modeled as sets of key words. If a suitable BK is not found for the given ontologies in the repository, the method searches the web for appropriate BK ontologies. In the likely case of returning more than one ontology, all found ontologies are used for the matching independently and a unified result set is produced. As reported, the adopted strategy aims at selecting the BK that maximizes the F-measure score for a given matching task, although no experimental results are presented to illustrate and support this selection criterium.

Positioning. We present the major points, which differentiate our technique as compared to the two approaches described above.

Although also relying on information retrieval techniques, in our method, the query is represented as a single document, built in the same way as the BKdocuments. This allows to avoid the complex weighted similarity computation in [START_REF] Quix | Automatic selection of background knowledge for ontology matching[END_REF], depending on the setting of two parameters. Instead of creating two classes of features (one for terms and one for structure), we embed the structure of the BKs and of the input ontologies in their respective textual representations (see Section 3), which has the potential to produce a more compact index.

We make clear distinction between query ontologies and BKs in the evaluation phase. Indeed, the evaluation presented in [START_REF] Quix | Automatic selection of background knowledge for ontology matching[END_REF] is highly biased by the fact that the authors use the same type of ontologies as queries and as BK (for example, if aligning two ontologies from the Benchmark track of OAEI, the authors would include the rest of the Benchmark ontologies as BK candidates), which will lead to having in the repository always a very useful BK source at hand. This is however, hardly a realistic scenario. In contrast, we use as BKs well-established and widely used knowledge graphs that are much likely to be called upon as BK sources for solving a real-life alignment problem. In that line of thought, our approach is generic and can handle different domains, contrarily to [START_REF] Faria | Automatic background knowledge selection for matching biomedical ontologies[END_REF].

In both [START_REF] Quix | Automatic selection of background knowledge for ontology matching[END_REF] and [START_REF] Faria | Automatic background knowledge selection for matching biomedical ontologies[END_REF] the BK selection appears to be strongly coupled with the actual matching procedure. One of the main motivations of work is to dissociate completely the BK selection process from the alignment procedure.

In contrast to our work, the results presented in [START_REF] Quix | Automatic selection of background knowledge for ontology matching[END_REF] are not reproducible, because no information is given regarding the selected BKs, neither about the similarity measure that has been used in the process. In turn, no direct experimental comparison to the approach is possible.

We could not make comparison between the works cited in this section by the fact that: -It is difficult to reproduce the scenarios presented in this papers -We do not use the same metrics -Our scenarios are not applicable on these approaches because they do not address the multi-domain selection and the multilingualism problems.

On another hand, the index built in our approach is reusable, no need to construct the index at each ontology matching tasks.

Conclusion and Future Work

In this work, we have addressed the problem of automatic selection of background knowledge sources for the task of ontology matching. We propose an approach using information retrieval techniques implemented in an automatic domain independent system that can handle multilingual input ontologies. We build an index for a set of known, well-established in the semantic web field knowledge sources, that are often used as BK for aligning ontologies. For a pair of ontologies to be matched, the selection process is a result of querying the indexed corpus for semantically similar BK sources from the indexed data. We provide an in-depth empirical study and we show that in certain cases the standard choice of a cosine similarity is not the most optimal and parameter free correlation measures can help discriminate better between close in terms of domains BK sources. We define an optimality criterium of selection based on the quality of the matching and we show experimentally that our approach satisfies this criterium. Contrarily to state of the art approaches, our technique has the advantage of not being based on a preliminary direct matching between the input ontologies.

In the future, we plan to work on optimizing the selection process by improving the quality of the index features. In that respect, we will consider the task of BK preselection for a particular domain, to be applied prior to the selection algorithm. We also plan to improve our selection criterium in order to take into account the trade-off between optimality and efficiency. Finally, we will investigate the benefits of the development of a BK selection method to assist the instance matching and link discovery processes.

Fig. 1 :

 1 Fig. 1: The BK indexing and selection process. The elements in dashed lines are not part of the selection workflow.

Table 1 :

 1 Anatomy and Large Biomedical Tasks

			Anatomy			Large Biomedical
		Cosin Pearson Spearman F-m Cosin Pearson Spearman F-m
	BabelNet	0.03	0.06	-0.76	0.05 0.0	0.0	-0.66	0.0
	DBnary	0.02	0.07	-0.72	0.0 0.02	0.02	-0.51	0.0
	DBpedia	0.01	0.01	-0.70	0.0 0.05	0.06	-0.60	0.0
	Doid	0.10	0.15	-0.14	0.66 0.15 0.14	0.40	0.53
	Uberon	0.26 0.33	0.40	0.79 0.16 0.14	0.5	0.60
	YaGo	0.01	0.01	-0.20	0.0 0.03	0.03	-0.22	0.0
	FMA	0.30 0.33	0.20	0.46	-	-	-	-

Table 2 :

 2 Conference and MultiFarm Tasks

			Conference		MultiFarm
		Cosine Pearson Spearman F-m Cosine Pearson Spearman F-m
	BabelNet	0.28	-0.08	0.73	0.61 0.30 0.39	0.44	0.49
	DBnary	0.06	-0.01	-0.34	0.46 0.16	-0.20	0.22	0.29
	DBpedia	0.1	-0.02	0.12	0.12 0.01	0.03	0.09	0.10

http://linkeddata.org

An Information Retrieval Approach to Automatic Selection of BKWe situate the BK selection problem in an information retrieval framework. We consider Γ as a corpus of documents and a given pair of ontologies s and t

http://oaei.ontologymatching.org/

https://ncit.nci.nih.gov/ncitbrowser/

http://kaiko.getalp.org/about-dbnary/

http://www.geonames.org/

http://do-wiki.nubic.northwestern.edu/do-wiki/index.php